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CONTRACT MECHANISMS FOR COORDINATING OPERATIONAL AND MARKETING DECISIONS IN A SUPPLY CHAIN
Contract Mechanisms for Coordinating Operational and
Marketing Decisions in a Supply Chain: Models & Analysis
Vijayender Reddy Nalla
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CONTRACT MECHANISMS FOR COORDINATING OPERATIONAL AND MARKETING DECISIONS IN A SUPPLY CHAIN
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CONTRACT MECHANISMS FOR COORDINATING OPERATIONAL AND MARKETING DECISIONS IN A SUPPLY CHAIN
NYENRODE BUSINESS UNIVERSITEIT
Contract Mechanisms for Coordinating Operational and
Marketing Decisions in a Supply Chain: Models & Analysis
Proefschrift
ter verkrijging van het doctoraat
aan de Nyenrode Business Universiteit
op gezag van de
Rector Magnificus, prof. dr. E.A. de Groot
en volgens besluit van het College voor Promoties.
De openbare verdediging zal plaatsvinden op
maandag 25 augustus 2008
des namiddags om vier uur precies
door
Vijayender Reddy Nalla
geboren op 31 maart 1978
te Hyderabad (India)
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CONTRACT MECHANISMS FOR COORDINATING OPERATIONAL AND MARKETING DECISIONS IN A SUPPLY CHAIN
Leescommissie
Promotores:
Prof. dr. V. Venugopal
Prof. dr. J.A.A. van der Veen
Overige leden :
Prof. dr. C. Rajendran
Prof. dr. J. Wijngaard
Prof. dr. K. Koelemeijer
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CONTRACT MECHANISMS FOR COORDINATING OPERATIONAL AND MARKETING DECISIONS IN A SUPPLY CHAIN
5
Acknowledgments
This PhD thesis is the result of almost five and a half years of honest effort at Nyenrode
Business Universiteit. Completing a Nyenrode PhD thesis was very interesting and
definitely challenging. As I write this acknowledgement I just cannot express the joy I am
going through in spite of a shortened hairline. A PhD thesis is not written by itself, but is
the result of the cooperation of many people. I would like to thank all those who have
helped during these PhD years and made writing this PhD thesis possible.
I would like to thank my Professor at IIT Madras, Dr. T.T Narendran, who believed in
my abilities and encouraged me to take the Nyenrode opportunity. This thesis piece
would not exist without Prof. Dr. Venugopal, as it is he who created this possibility, took
me in and has been helpful ever since. Both he and Prof. Dr. Jack van der Veen have
taken my research very seriously in spite of their busy schedules and at the end made sure
that the best possible output was obtained. I can imagine how difficult it must have been
personally for them to get such an output from me. I thank both of them for their
patience, and their willingness to help me out on each and every hurdle I have
encountered during this challenging process. They have not only contributed to enhance
my research capabilities, but have trained me to pursue every job with clarity and
passion. Without them not even a single page of this thesis would have achieved the form
that it has today. I would also like to thank the other members of the examination
committee (Prof. Dr. C. Rajendran, Prof. Dr. Jacob Wijngaard and Prof. Dr. Kitty
Koelemeijer) for giving their valuable time to review this dissertation.
It is hard for me to find words to express my gratitude to my parents, who have always
believed in my potential and given me the freedom to make my decisions, as well as
extended their full support during this long PhD journey. I would like to express my
sincere gratitude to my fiancée G. Renuka, who has given me encouragement and support
during the finalization of this piece.
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TABLE OF CONTENTS
There are two people who deserve special mention in this thesis. The first one is my
dearest friend Vikrant, who stood by me in all the tough times I went through during the
PhD process. Vikrant, I am very grateful to you for your friendship and the affection that
you have for me. Then, I would like to thanks my dear friend and colleague Ms. Duijvis
with whom I had the privilege of sharing the office for almost four years. She never made
me feel that I was in a different country, and her advice on all practical issues was
invaluable. Her faith in my abilities and her encouragement has helped me overcome the
difficult phases of my research. Thank you Ms. Duijvis, I value your contribution very
highly.
A special mention of Prof. Venugopal and his family (Bhooma madam, Hema and
Anand), who have always considered me as a part of their family, and have helped me on
numerous occasions during my entire stay in the Netherlands. My special thanks to Dr.
Sharda for considering me as one of her family members and inviting me to her place for
all significant Indian festivals. Then to my good friends (Sisir, Ajay, Rens, Zaka khan) in
the Netherlands who have added a very interesting social dimension to my life and to all
Nyenrodians who have made my stay at Nyenrode very pleasurable.
Living in Breukelen is per se a fantastic experience. One of the biggest motivations for
me to stay in the Netherlands is this beautiful village which has provided me with nothing
but very positive experiences. In this village, my second home, I did meet many special
and interesting people. At this point Mr. Vital and his family come foremost to my mind,
as he enacted the role of my local guardian perfectly.
I am very thankful to the Nyenrode Research group for providing extra research time. I
am thankful as well to the library staff for helping me with all the material required for
this research. The staff of the personnel department has played a crucial role for timely
arrangement of all the permits. I am very thankful to Anna for helping me with the
English and Tasja for working on the layout and the design of this dissertation. My
special thanks to Jacqueline and her team who played a very significant role in the final
stages.
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TABLE OF CONTENTS
Table of Contents
CHAPTER 1
11
INTRODUCTION
11
1.1
1.2
1.3
1.4
1.5
1.6
1.7
11
13
15
17
20
23
25
BACKGROUND
SUPPLY CHAIN MANAGEMENT DEFINED
SC COORDINATION APPROACHES
RESEARCH FOCUS AND MOTIVATION: DEFINING THE BOUNDARY
SUPPLY CHAIN CONTRACTS AS COORDINATION MECHANISM: A BRIEF REVIEW
RESEARCH QUESTIONS, FRAMEWORK AND METHODOLOGY
CONTRIBUTION OF THE THESIS
CHAPTER 2
27
LITERATURE REVIEW
27
2.1
2.2
2.2.1
2.2.2
2.2.3
2.2.4
2.3
2.3.1
2.3.2
2.3.3
2.4
2.4.1
2.4.2
2.4.3
2.5
2.6
27
29
29
32
34
37
42
43
44
45
47
49
50
52
53
56
INTRODUCTION
COORDINATING PRICING AND REPLENISHMENT DECISIONS IN SUPPLY CHAINS
WHOLESALE PRICE CONTRACT
REVENUE AND PROFIT SHARING CONTRACTS
QUANTITY DISCOUNTS & THE LICENSE FEE MECHANISM
BUY-BACK (RETURN POLICIES)
PROMOTIONAL MECHANISMS FOR COORDINATED DECISIONS IN SUPPLY CHAINS
TRADE PROMOTIONS
CONSUMER REBATES
DIRECT REBATES
COORDINATING THE SERVICE (QUALITY) DECISIONS IN SUPPLY CHAINS
WHOLESALE PRICE CONTRACT + COST SHARING
REVENUE SHARING/ROYALTY PAYMENTS
QUANTITY DISCOUNTS AND TWO-PART TARIFF CONTRACTS
COORDINATING PRODUCT-LINE DECISIONS IN SUPPLY CHAINS
CONCLUSIONS & THE RELEVANCE OF THE CHAPTERS 3-9
PART 1: CONTRACT MECHANISMS FOR COORDINATING PRICING AND
REPLENISHMENT DECISIONS IN A SUPPLY CHAIN
61
CHAPTER 3
63
COORDINATING PRICING AND REPLENISHMENT DECISION IN A PRICE
SENSTITIVE DETERMINISTIC SC
63
3.1
3.2
3.3
63
66
67
INTRODUCTION
MODEL AND BASIC ANALYSIS
THE CENTRALIZED SCENARIO
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3.4
3.5
3.6
3.7
3.7.1
3.8
3.9
3.10
TABLE OF CONTENTS
THE SOLITAIRE SCENARIO
THE PARTNERSHIP SCENARIO
CONTRACT MECHANISMS
REVENUE SHARING MECHANISM
METHODS TO DIVIDE THE OVERALL IMPROVED PROFIT
PROFIT SHARING MECHANISM
QUANTITY DISCOUNT & LICENSE FEE MECHANISM
CONCLUSIONS
68
71
75
75
78
81
84
87
CHAPTER 4
89
COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY
CHAIN WITH INCREASING MARGINAL COST
89
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
INTRODUCTION
MODEL AND BASIC ANALYSIS
SOLITAIRE SCENARIO ANALYSIS
INTRA-FIRM TRANSFER PRICING MECHANISMS
REVENUE SHARING MECHANISM
PROFIT SHARING MECHANISM
QUANTITY DISCOUNT & LICENSE FEE MECHANISM
CONCLUSIONS
90
91
93
97
100
103
106
109
CHAPTER 5
111
COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY
CHAIN WITH TWO CONSUMER SEGMENTS
111
5.1
5.2
5.3
5.3.1
5.4
5.5
5.6
111
113
118
121
123
125
128
INTRODUCTION
MODEL AND BASIC ANALYSIS
DIRECT REBATE AS COORDINATION MECHANISM
PUSH-PULL DISCOUNTS
REVENUE SHARING
PROFIT SHARING
CONCLUSIONS
CHAPTER 6
129
COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH
UNCERTAIN DEMAND
129
6.1
6.2
6.3
6.4
6.5
6.6
INTRODUCTION
MODEL AND BASIC ANALYSIS
CONTRACT MECHANISMS
REVENUE SHARING MECHANISM
PROFIT SHARING MECHANISM
LICENSE FEE MECHANISM
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130
137
137
141
144
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6.7
6.8
BUY-BACK CONTRACTS
CONCLUSIONS
9
147
152
PART 2: CONTRACT MECHANISMS FOR COORDINATING PROMOTIONAL
DECISIONS IN A SUPPLY CHAIN
155
CHAPTER 7
157
USING PROMOTION MECHANISMS TO COORDINATE DECISIONS IN A SUPPLY
CHAIN WITH PRICE SENSITIVE DEMAND
157
7.1
7.2
7.3
7.4
7.4.1
7.5
7.6
INTRODUCTION
BASIC MODEL AND ANALYSIS
MAIL-IN-REBATE
WHOLESALE PRICE DISCOUNT ANALYSIS
MAIL-IN-REBATE VS WHOLESALE PRICE DISCOUNT
COMBINED REBATE MECHANISM
CONCLUSIONS
157
158
161
166
168
172
176
PART 3: CONTRACT MECHANISMS FOR COORDINATING PRICE AND SERVICELEVEL DECISIONS IN A SUPPLY CHAIN
177
CHAPTER 8
179
COORDINATING MECHANISMS FOR A SUPPLY CHAIN FACING PRICE AND
SERVICE-LEVEL SENSITIVE DEMAND
179
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
8.9.1
8.9.2
8.10
180
182
184
186
191
197
202
208
209
211
212
214
INTRODUCTION
MODEL IN WHICH THE BUYER DECIDES THE LEVEL OF SERVICE PROVISION
CENTRALIZED SCENARIO
SOLITAIRE SCENARIO ANALYSIS (DECENTRALIZED CHANNEL)
REVENUE SHARING MECHANISM
PROFIT SHARING
QUANTITY DISCOUNT MECHANISM
LICENSE FEE MECHANISM
MODEL WHERE THE SUPPLIER DECIDES THE SERVICE PROVISION
SOLITAIRE SCENARIO ANALYSIS
CONTRACT MECHANISMS
CONCLUSIONS
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TABLE OF CONTENTS
PART 4: CONTRACT MECHANISMS FOR COORDINATING PRODUCT LINE
DECISIONS IN A SUPPLY CHAIN
217
CHAPTER 9
219
USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
219
9.1
9.2
9.3
9.4
9.5
9.6
9.7
9.8
INTRODUCTION
MODEL AND BASIC ANALYSIS
CENTRALIZED SCENARIO ANALYSIS
SOLITAIRE SCENARIO
SLOTTING ALLOWANCE MECHANISM
REVENUE SHARING MECHANISM
PROFIT SHARING MECHANISM
CONCLUSIONS
220
222
224
226
235
239
246
248
CHAPTER 10
251
CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
251
10.1
10.1.1
10.1.2
10.1.3
10.1.4
10.2
10.3
10.4
252
252
255
256
256
257
258
259
RESEARCH FINDINGS AND CONCLUSIONS
COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC (PART I)
COORDINATING PROMOTIONAL DECISIONS IN A SC (PART 2)
COORDINATING PRICE AND SERVICE-LEVEL DECISIONS IN A SC (PART 3)
COORDINATING PRODUCT LINE DECISIONS IN A SC (PART 4)
OVERALL CONCLUSIONS
IMPLEMENTATION ISSUES
DIRECTIONS FOR FURTHER RESEARCH
REFERENCES
261
SUMMARY IN ENGLISH
269
NEDERLANDSE SAMENVATTING
275
CURRICULUM VITAE
283
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INTRODUCTION
Chapter 1
Introduction
Chapter synopsis
This dissertation discusses a range of operational and marketing decisions at various
stages within a Supply Chain (SC). One of the most important problems in any SC
consisting of autonomous organizations is sub-optimization due to the fact that the SC
decision making is distributed over the various players. In such a setting, so-called
coordinating mechanisms might be useful. Ideally, contract mechanisms ensure that the
SC is optimized as if it were a single unit (coordination) and is designed such that all
players benefit from working together through the coordinating mechanism (win-win). As
this dissertation will discuss several contract mechanisms in various SC settings and for
different types of decisions, this introductory chapter sets the stage for such analysis.
More specifically, in this chapter we will introduce the research problem and its scope
and background, the research framework (definition, conceptual model and focus) and the
contributions made by this dissertation to the academic and managerial communities.
1.1 Background
Companies in the past perceived themselves as stand-alone entities in the business
environment. Times have changed. To stay competitive in the current complex and
dynamic business environment, companies have begun to perceive themselves as part of a
chain or network of companies. The reason is simple: companies are so intertwined and
dependent on each other that no single company can survive and prosper on its own
without deep cooperation and collaboration. Some possible reasons for the increased
interdependence among different companies are:
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x
CHAPTER
1
More and more emphasis is given to “core business” and added value to the core
business: Focusing on the core competence implies that non-core activities can be
outsourced; an organization cannot excel at all activities and therefore should seek
others who can do better. The result is that chains get longer;
x
Opening up of borders (e.g., within the European community); development of the
Far East. Through these developments, “global sourcing” has become a reality,
leading to an increase in outsourced (or off-shored) activities, and hence longer
supply chains (see also the best-seller “The World is Flat” by Friedman, 2005);
x
The rapid developments in information and communication technology (ERP,
internet, et cetera) have made it more feasible to have several operating units around
the globe, again enabling longer chains.
With the increased length of chains and the increased interdependencies between
organizations, coordinating between such entities has become an important managerial
challenge. This has led to considerable interest among both practitioners and academics
in the field of Supply Chain Management (SCM). Leading companies such as Procter &
Gamble, Wal-Mart, Boeing, Cisco and HP view SCM as a critical driver to maximize
shareholder value. To manage the challenges due to interdependencies within their supply
chains, these leading companies constantly look for opportunities to collaborate with their
trading partners and thus enhance their added value while simultaneously decreasing their
costs, resulting in higher profits. But not all companies are equally confident of the
benefits of such collaboration and are also not confident about how and in what areas to
collaborate. This has motivated us to pursue this research work. In this dissertation, we
explore a specific type of coordinating mechanisms for selected operational and
marketing decision problems and illustrate the benefits of such collaborative mechanisms.
In this chapter, we set the stage for the entire thesis by defining supply chain
management, defining the focus and scope of our work, defining the problem statement
and research questions, and developing and discussing our research framework.
The remainder of this chapter is organized as follows. We start with defining SCM and an
overview of SC coordination approaches, after which the research focus and its
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INTRODUCTION
13
motivation are given. In Section 1.5, the SC contract mechanisms are reviewed.
Subsequently, the research questions, research framework and research methodology are
discussed. We close the chapter with a statement of how the thesis contributes to the
academic literature and managerial insights.
1.2
Supply Chain Management defined
Unfortunately, although generally a SC is defined as a network of many entities, each
dependent on others in fulfilling their customers’ requests, the literature does not provide
a unified definition of SCM. In order to derive a definition of SCM for this dissertation,
we have studied two papers that provide a literature review on SCM definitions, namely
Betchel & Jayaram (1997) and Mentzer et al. (2001). Furthermore, for the same purpose
we reviewed the classic paper Spengler (1950), since this paper is frequently seen as the
source of the literature on SC coordination mechanisms. In reviewing these papers, it
became clear that the core focus of SCM is on “cost containment”, “revenue
enhancement” and “coordination”. Synthesizing these articles has lead to the definition of
SCM used in this dissertation, namely: The coordination of different business entities in
the supply chain to reduce waste (costs) and create value to customers and thus enhance
revenues. Here, coordination refers to managing challenges due to interdependencies
among business entities by aligning goals, processes/functions, decisions and activities
(see Figure 1.1). For example, to reach the common goal of just-in-time Production,
Toyota Motor Corporation and its seat supplier Johnson & Control have aligned their
production process, lot-sizing decisions and their production planning activities. In
general, we can say that if products and services are to be supplied to the market
efficiently and effectively, then business entities need to align their fulfillment process
and coordinate their decisions on capacity, inventory, pricing, and promotion, quality of
the product or service, and product variety.
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CHAPTER
Aligning
Activities
Aligning
Decisions
Aligning
Processes
1
Aligning
Goals
Increased Complexity
Figure 1.1: Components of Coordination
Depending on whether the business entities are departments within a company, businessunits within a corporation, or separate autonomous organizations, we can define a SC at
three levels (Figure 1.2). The first level of SCM refers to the coordination of the different
functions (or departments) within a company such as research and development (R&D),
marketing and sales (M&S), operations and logistics (O&L) and purchasing. At this level,
the most commonly used coordination mechanism to manage dependencies is the use of
cross-functional teams.
The second level of SCM refers to the coordination of different business-units (BU’s)
within one corporation that produce and distribute components for several products. SCM
at this level is aimed at optimizing the flow of goods, information, activities and goals
among different business units. The business units can be country specific, product
specific, or both. Consider the case of Philips which is divided into separate businesses,
such as the consumer electronics, lighting and medical systems. Similarly, Unilever
classifies its businesses as cooking and eating, healthy living, beauty and style, and
around the house. At this level, the most commonly used coordination mechanisms to
manage dependencies are the use of vertical supervision by top management or the use of
transfer pricing.
At the third level of SCM, the different business entities are autonomous organizations.
SCM at this level implies that several independent organizations work together to
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INTRODUCTION
improve the results of all the players. Establishing coordination at the third level is a
difficult and challenging task as the SCs at the third level do not have owners, and the
entities are independent autonomous organizations with their own objectives.
Coordination
across functions
within a company
Coordination
across divisions
within a Corporation
Level 1
Level 2
Coordination
across companies
Level 3
Increased Complexity
Figure 1.2: Different levels of SCM
1.3
SC coordination approaches
Organizations seek to achieve coordination through different approaches. The first step
towards establishing coordination might be to share information between the entities in
the SC. The sharing of information is indeed a necessary condition but may not be
sufficient to achieve coordination and improve overall SC performance. Hence, besides
sharing of information, organizations can use two main approaches to achieve
coordination. The first approach is to modify the governance structure of the trading
relationship, for example, by modifying the ownership (i.e., “who owns what”) and/or by
modifying decision rights (i.e., “who decides what”). Modifying the governance structure
works only when the process owner gets the decision rights over the functional people.
This approach is the most difficult approach to implement, especially at the third level of
SCM.
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1
The second approach for achieving coordination within the SC is to modify the terms of
trade. The modification of the terms of trade is achieved through incentive schemes or
contracts over certain trade parameters (variables). This approach aims to achieve
coordination among business entities by providing incentives to share risks and/or
rewards. There are several contract mechanisms that can be designed and used to make
sure that the independent decisions made by business entities optimize the overall
performance of the whole chain (in such a case, we say that the mechanism coordinates
the chain). This approach is quite useful at all three levels of SCM. The use of the socalled buy-back contract for sharing risk and the profit sharing contract for sharing
reward are two examples of the contract mechanisms, which can be applied for
coordination and win-win opportunities at different levels of the SC. The contracts must
enable all independent business entities to improve their performance when compared to
an uncoordinated situation. In such a case, we say that the contract mechanism leads to a
win-win situation.
The choice of appropriate contract mechanism depends on several factors including
product characteristics (demand uncertainty, lifecycle of the product, margin, et cetera),
balance of power and degree of dependency, and level of operational risk cost and risk
averseness of the players in the SC. For example, for fashion products such as apparel
and consumer electronics, the replenishment lead time is too long, demand tends to be
more uncertain, the overstocking cost is high and hence the Buyer (retailer) typically
responds by under-stocking. This situation is usually more expensive for the Supplier
(manufacturer) as the margins for fashion products tend to be on the higher side. The
Supplier would therefore be interested to induce the Buyer to buy more. The Supplier can
easily induce the Buyer by providing incentives that minimize the overstocking risk for
the Buyer. One such incentive mechanism is the buy-back incentive which allows the
Buyer to return the unsold products. Hence, the second approach would be more
appropriate than the first in this case. On the other hand, for functional products such as
milk, cereal, and juice, demand tends to be fairly stable; the margin tends to be low and
can be replenished on a daily or weekly basis. For such types of products, the Buyer
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INTRODUCTION
could transfer the responsibility of the replenishment process to the vendor to ensure that
products are supplied efficiently.
Decentralization:
No Coordination
Information
sharing
Level 1
Less powerful
in reaching
Optimal SC Performance
Modify terms
of trade Risk Sharing
Reward Sharing
Level 2
Modify
Governance
structure
Level 3
Centralized
Level 4
More difficult
to implement
Figure 1.3: Continuum of SC coordination approaches
Figure 1.3 represents a continuum of coordinating mechanisms. The left-most side of the
continuum represents a traditional arms-length relation with no coordination. The rightmost side of continuum represents a completely centralized situation, where business
entities in SCM are considered operating as a single entity. Between these two extremes
other coordinating mechanisms are given. The further to the right on the continuum, the
more difficult the mechanisms are to implement, as they require a more intense and
involving partnership. The farther to the left on the continuum, the less powerful the
mechanisms are in coordinating the business entities and optimizing the SC. It can be
observed that a first step towards coordination is to share information among the involved
SC parties and hence it is a necessary condition for all other coordination mechanisms.
In the next section, we define our research focus and our motivation for such a focus.
1.4
Research focus and motivation: Defining the boundary
Referring to the discussions and framework in previous sections, this dissertation will
focus on the third level of SCM. As discussed earlier, creating coordination involves
aligning activities, decisions, processes and goals. This research focuses on the
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1
coordination component, namely aligning decisions. More specifically, this doctoral
dissertation focuses on aligning decisions in the areas of logistics/operations and
marketing. This doctoral research focuses on one of the approaches, namely modifying
the terms of trade in order to establish SC coordination. The focus of this dissertation is
summarized in Figure 1.4.
Coordination
across functions
within a company
Coordination
across divisions
within a Corporation
Level 1
Coordination
across companies
Level 2
Level 3
Different levels of Supply Chain: Our focus
Different levels of a Supply Chain: Our focus
Aligning
Activities
Aligning
Activities
Aligning
Decisions
Aligning
Decisions
Aligning
Processes
Aligning
Processes
Aligning
Goals
Aligning
Goals
Coordination components: Our focus
Decentralization:
No Coordination
Information
sharing
Modify terms
of trade Risk Sharing
Reward Sharing
Modify
Governance
structure
Centralized
Approaches to establish SC coordination: Our focus
Figure 1.4: The focus of this dissertation
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INTRODUCTION
19
In short, the focus of this dissertation is on modeling and analyzing contract mechanisms
for coordinating the operations and marketing decisions of business entities at Level 3 of
SCM. This dissertation aims to contribute to the understanding of how contracts can
coordinate operational and marketing decisions across organizations and lead to win-win
situations. This makes our study managerially more relevant. In this thesis we specifically
look for the following two things:
1. SC optimization (or SC coordination) : Maximum total SC profit is achieved
2. Win-win: All the players in the SC benefit
A SC is said to be coordinated if it achieves the same profit as in a centralized situation
(or full partnership). Furthermore, win-win is said to be achieved if all the players make
greater profit compared to the decentralized decision making situation. It is to be noted
that one does not imply the other; a coordinated SC might fail to provide additional profit
to one of the players. Also, even if all players gain from their collaboration, the SC is not
necessarily optimized. Most of the literature seems to focus on achieving SC coordination
while ignoring the win-win component. However, when the SC consists of autonomous
organizations (which is assumed at Level 3), clearly, from an implementation point of
view, win-win is probably more important than SC coordination. After all, the player is
only willing to participate in joint actions if he will gain from the collaboration.
Furthermore, since the SC as a whole is nobody’s specific focus, the optimal SC result
can be seen as less important from a practical point of view.
The motivation for our focus partly comes from the increasing trend of outsourcing value
chain activities in different industries (Friedman, 2005). One of the fundamental
problems in management is to decide between centralization (hierarchical decision
making) and decentralization (decisions made at the lowest possible level). Everybody
agrees that decentralized decision making is important, because at the lower level, people
can best judge what works at their organization. Yet decentralization also inevitably leads
to sub-optimization, a situation that can be avoided by centralized decision making. In a
way contract mechanisms offer a solution to this dilemma. They are designed so that an
optimal decentralized decision is automatically an optimal centralized decision. It is this
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1
piece of magic that we try to explore. These contract mechanisms are powerful enough to
create SC optimization and win-win scenarios, and implementation is not too difficult in
most of the cases. This study is meant to help and support companies in understanding
the impact of different contractual mechanisms and help companies to design contracts
that enhance the efficiency and effectiveness of their SC.
Decision \ Methods Info sharing
Modify
Terms of Trade
Modify
Governance Structure
Capacity
decision
Replenishment
Decision
Quality
Decision
Pricing
Decision
Other
Figure 1.5: SC Coordination - A simplified Taxonomy & our research focus
This dissertation is based on a decision area spectrum and coordination approaches
spectrum, and uses the simplified taxonomy shown in Figure 1.5 to study SC
coordination mechanisms.
1.5
Supply Chain Contracts as coordination mechanism: A brief review
The focus of this dissertation is on modeling and analyzing contract mechanisms for the
coordination of operations and marketing decisions of business entities at Level 3 of
SCM. This dissertation aims to contribute to the understanding of how contracts can
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INTRODUCTION
21
coordinate operational and marketing decisions across organizations and lead to win-win
situations. In this section we provide a brief review of the SC contract mechanisms.
A Supply Chain contract is an agreement among different organizations/entities with
respect to different trade parameters such as pricing, order quantity commitment,
periodicity of ordering, delivery commitment quality, and information sharing that
together define the terms of trade. For example, the agreement with respect to the pricing
parameter usually concerns:
x
How much is paid for each unit.
x
What additional incentives are involved and how they are paid. This part can include
agreement on incentives such as quantity discount, profit sharing, revenue sharing,
credit for returned goods, et cetera.
The format of SC contracts varies across industries. Some of the commonly observed SC
contracts include the quantity discount contract, profit sharing contract, revenue sharing
contract and the buy-back contract.
Any SC contract must be designed to:
x
Specify incentive to induce the behavior of SC players: reduced wholesale price,
quantity discounts, profit sharing and revenue sharing.
x
Induce the players to share risk: The Buyer and the Supplier share the risks arising
from various sources of uncertainty (e.g., market demand, selling price, product
quality, delivery time, et cetera). The minimum order quantity contract often protects
the Supplier whereas the buy-back contract usually protects the Buyer.
x
Make the terms of trade explicit: (e.g., lead times, on-time delivery, and conformance
rates, et cetera) as well as specifying penalties for non-cooperative behavior.
x
Improve system-wide performance /chain coordination.
The effect of a SC contract on the performance of individual players and the SC depends
on factors such as:
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x
CHAPTER
1
Supply Chain Structure:
o # of stages in the SC;
o # of players in each stage (competition);
o # of consumer segments;
o Who has the power in the SC;
o Who holds which information (e.g., symmetric versus asymmetric
information).
Our study focuses mainly on the two-echelon SC with a Supplier and a Buyer catering to
a consumer base. In some of our models, we have considered segmentation in the endconsumer demand.
x
Product characteristics:
o Perishable product (# of replenishments: one-time versus multiple);
o Presence of substitute product;
o Life cycle of the product;
o Product quality.
In our study we focus mostly on single replenishment. We also consider a case which
consists of multiple product variants.
x
Demand Characteristics:
o Demand uncertainty;
o Variation;
o Whether back ordering is possible;
o Batching.
In our study, we consider mostly deterministic and price sensitive demand. We also
address the pricing and replenishment decision in a stochastic setting.
x
Supply Characteristics:
o Supply capacity;
o Number of suppliers;
o Reliability of suppliers.
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INTRODUCTION
23
Our study considers a single supply source with no supply uncertainty.
Chapter 2 reviews the literature on contracts used for coordinating different operational
and marketing decisions in a SC. We make the following observations based on our
extensive literature study:
x
Most of the earlier studies on contracts focus more on pricing and inventory
decisions. Not much work has been done with respect to the other operational and
marketing decisions from the perspective of SC coordination.
x
Although a few studies mathematically do address the issue of SC coordination, the
existence of win-win scenarios is almost never shown explicitly. Recall that from an
implementation point of view, win-win scenarios are more important than SC
coordination yet typically in the literature only SC coordination is studied.
x
Most of the earlier studies have ignored the possibility of using a combination of
contractual types for a situation and hence ignored the combined effect of contractual
agreements.
x
Earlier studies have not attempted to understand the relationship between different
contract types.
This dissertation draws on these observations and contributes to the literature by filling in
some of the above mentioned gaps. In the next section we present the problem statement,
the research framework, and the methodology used for this dissertation.
1.6
Research questions, framework and methodology
This dissertation aims to address the following problem statement:
Can we use contracts to coordinate operational and marketing decisions within and
across organizations under different demand and supply conditions and achieve a winwin situation?
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CHAPTER
1
Control Variables
Supply Chain
Structure
C
o
n
t
r
a
c
t
s
Product
Demand
Characteristics Characteristics
Supply
Characteristics
Operational Decisions
Replenishment decision;
Capacity decision;
Quality Decision;
Marketing Decisions
Coordination ?
&
Win-Win?
Pricing decision;
Promotional decision;
Figure 1.6: Research Framework
The research framework that will be used for this dissertation is presented in Figure 1.6.
We make use of different control variables such as SC structure, product characteristics,
demand characteristics, and supply characteristics to create different SC settings. We
address those decisions that need to be coordinated in different SC settings. We
specifically make use of contracts to achieve coordination and win-win scenarios within
the chosen SC settings for different operational and marketing decisions.
To address the central problem statement, the following research questions will be
addressed:
For a given decision problem and for the given values of the control variables:
1)
Which contracts coordinate the SC and lead to win-win situations?
2)
Which contract is the best for the different players and the SC? Why?
3)
Is it worthwhile to use a combination of different contract types? If so, which
combination will be meaningful? What would be the combined effect on SC
performance?
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INTRODUCTION
4)
25
Is there a “relationship” among different contractual forms? If so, how can it be
used from an implementation perspective?
The research questions mentioned above will be addressed through analytical modeling.
Most of the literature on contract design has used analytical modeling as research
methodology. We follow along the same lines and make use of an operations research
type of optimization (local versus global optimization), simple economic analysis, and
basic differential calculus as the tools for designing contract mechanisms. The
appropriate tools are selected depending on the SC setting and the decisions that need to
be coordinated. We have used previous literature as a guideline in choosing the
appropriate analytical tools for the design of contracts.
1.7 Contribution of the thesis
This section briefly outlines the theoretical contributions and the managerial relevance of
the results obtained in this thesis.
Theoretical contribution:
1) This study addresses a wide range of decisions at the interface of operations and
marketing in a variety of SC settings. The decisions we address in this thesis are: (a)
pricing and replenishment decisions, (b) promotional decisions, (c) service-level or
quality decisions, and (d) product variety decisions.
2) In all the above decisions we explicitly address the issue of whether win-win
situations always exist when contracts are used. Literature concerning this issue is
almost nonexistent.
3) We apply a wide range of contract mechanisms and try to identify the relationships
that exist among them. We also discuss these mechanisms from an implementation
perspective.
4) The impacts of different SC settings on the performance of contract mechanisms have
been studied.
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5) This study presents strong theoretical insights, with the possibility for extensive
practical use by SC managers in the future.
Managerial relevance and contribution
1) The decisions that are covered within this thesis (pricing and replenishment,
promotions, service-level or quality, and product line decisions) are critical to SC
managers.
2) This study helps the SC manager to realize and understand the potential of the
contract mechanisms.
3) When more than one mechanism coordinates and provides win-win scenarios, we try
to identify mechanisms which are easier to implement.
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INTRODUCTION
Chapter 2
Literature Review
Chapter Synopsis
In this chapter, we review the coordination literature for different Supply Chain (SC)
decisions such as pricing, replenishment, promotions, service quality, and product line
decisions.
2.1
Introduction
Optimal Supply Chain (SC) performance requires the execution of a set of decisions
optimal for the SC. Unfortunately, SC members often make decisions with self-serving
focus by optimizing their own objectives. This often results in poor SC performance. As
indicated in the first chapter, there are three different approaches for coordinating SC
decisions. They are: (1) information sharing, (2) modifying the terms of trade (contract
mechanisms), and (3) changing the governance structure. Table 2.1 summarizes the
coordination framework for different decisions.
Decisions \
Approaches
Pricing and
Replenishment
Promotion
Quality of
Service
Product line
decision
Information sharing
Modifying the terms of trade
(contract mechanisms)
Changing the governance
structure (Partnership)
Table 2.1: Coordination framework for selected SC decisions
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As this dissertation focuses on the approach of modifying the terms of trade, this chapter
reviews the SC literature on contract mechanisms. Coordination with contracts or
coordinating by modifying the terms of trade has not only been addressed in operations
and marketing literature but also in other pieces of literature like economics and law,
industrial organization et cetera. However, our review is limited to the literature in the
area of operations and marketing, i.e., we have not looked at the literature related to
contracts in other areas.
Decisions\
Contract types
Pricing and
Replenishment
Promotion
Quality of
Service
Product line
decision
Wholesale price contract
Revenue sharing
Profit sharing
Quantity discount mechanism
License fee mechanism
Buy-back contract
Other Contracts
Table 2.2: Framework for literature review
We have classified the literature on contract mechanisms that are used to coordinate
pricing, replenishment, promotions and product-line decisions based on the framework
given in Table 2.2. The relevant contributions of selected studies are discussed in detail,
and the limitations of each study are highlighted wherever possible. In Section 2.2, we
discuss the literature on contract mechanisms for coordinating pricing and replenishment
decisions. Later in Section 2.3, we discuss the literature on promotions mechanisms. We
then outline the literature on contract mechanisms for coordinating quality or servicelevel decisions in Section 2.4. In Section 2.5, we discuss the literature that uses contract
mechanisms to coordinate product line decisions. Finally, we conclude the literature
study.
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LITERATURE REVIEW
2.2
29
Coordinating Pricing and Replenishment Decisions in Supply Chains
In this section, we review the coordination literature related to pricing and replenishment
decisions in Supply Chains. We classify the literature in Table 2.3 based on the type of
contract mechanisms used.
In each of the next sub-sections, we provide a summary of the literature mentioned in
Table 2.3. We discuss the contributions of each study and outline the limitations
wherever possible.
2.2.1 Wholesale price contract
With a wholesale price contract, the Supplier (manufacturer) charges the Buyer (retailer)
a wholesale price W per unit purchased. Most studies on contracts start their analyses
with the wholesale price contract, as it is the most commonly used contract in practice.
The wholesale price contract is very simple to administer. However, for the wholesale
price contract to coordinate the SC, the Supplier must be willing to supply the product at
his marginal cost, which leaves his profit at zero. Spengler (1950) was the first to identify
the problem of “double marginalization” in a serial supply chain. He argued that a serial
SC sees a coordination failure because there are two margins, and neither firm considers
the entire Supply Chain’s margin when making a decision.
Hirshleifler (1956), and later Ronen & McKinney (1970), considers the pricing and
replenishment decisions in a Supply Chain (SC) in which both the Buyer and the Supplier
incur increasing marginal costs which are represented by quadratic functions of their
ordered/produced quantities. They suggest internal wholesale price (transfer pricing)
mechanisms to coordinate replenishment decisions among the different divisions of the
same firm.
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Jeuland & Shugan (1983); Monahan (1984); Rosenblatt & Lee (1985); Rosenblatt (1986);
Bannerjee (1986);Moorthy (1987); Weng (1995); Raju & Zhang (2005)
Ingene & Parry (1995); Ingene & Parry (2000); Chen et al. (2001); Raju & Zhang (2005);
Burnetas et al. (2007)
Pasternack (1985);Marvel & Peck (1995); Kandel (1996); Emmons & Gilbert (1998);
Padmanabhan & Png (1997); Donohue (2000); Webster & Weng (2000); Tsay (2001);
Krishnan et al. (2004); Yao et al. (2005); Wang et al. (2007)
Quantity discount
mechanism
License fee
mechanism
Buy-back contract
Promotion
Table 2.3: Literature on contract mechanisms to coordinate pricing
and replenishment decisions
Jeuland & Shugan (1983); Van der Veen & Venugopal (2001)
Spengler (1950); Hirshleifler (1956); Ronen &McKinney (1970); Gerstner & Hess (1991);
Anupindi & Bassok (1999); Van der Veen & Venugopal (2000); Lariviere & Porteus (2001);
Cho & Gerchak (2001); Dong & Rudi (2001); Bernstein et al. (2002)
Dana & Spier (2001); Pasternack (2001); Wang et al. (2004); Gerchak & Wang (2004);
Wang & Gerchak (2003); Van der Veen & Venugopal (2005); Cachon & Lariviere (2005);
Koulamas (2006)
Pricing and Replenishment
Profit sharing
Revenue sharing
Wholesale price
contract
Decision/Terms of
trade
Quality of
Service
Product
line
decision
30
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2
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LITERATURE REVIEW
31
Gerstner & Hess (1991) have looked at the effectiveness of a wholesale price discount in
channel coordination in a setting where the market is made up of two different consumer
segments: high willingness-to-pay consumers and low willingness-to-pay consumers.
Several studies exist which analyze the sensitivity of a wholesale price contract in
different SC settings. In one such study, Anupindi & Bassok (1999) analyze the
wholesale price contract in a setting where the Supplier sells to a retailer who faces an
infinite succession of identical selling seasons. There is a holding cost on left-over
inventory at the end of a season, but inventory can be carried over to the next season. The
retailer submits orders between seasons, and the Supplier is able to replenish
immediately. Within each season the retailer faces a newsvendor problem with the tradeoff between lost sales and inventory holding costs. In the above setting, the study shows
that the Supplier’s wholesale price is lower than in a single season model. They conclude
that the wholesale price contract performs better in a multi period model than in a single
period model.
Van der Veen & Venugopal (2000) perform an extensive analysis to demonstrate the
double marginalization phenomena. In addition, they have also proposed a partnership
scenario under which the above phenomena can be eliminated.
Lariviere & Porteus (2001) perform an extensive analysis of the wholesale price contract
in the context of the newsvendor problem. They claim that as the relative demand
variability decreases, the retailer’s price sensitivity decreases, the wholesale price
increases, and the decentralized system becomes more efficient (i.e., captures a greater
share of potential profit). The manufacturer’s share of realized profit also increases and
the retailer’s profit drops considerably. The authors also explore factors that would lead
the manufacturer to set an optimal wholesale price which would maximize her profit.
Cho & Gerchak (2001) and Bernstein et al. (2002) argue that marginal cost pricing does
not necessarily lead to zero profit for the Supplier when the marginal cost is not constant.
Dong & Rudi (2001) study the wholesale price contract with two newsvendors and a
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possibility of transshipment of inventory between them. They show that the Supplier is
generally able to capture most of the benefits of transshipments and the retailers are
worse off with transshipments.
In the next subsection, we address the literature on revenue and profit sharing
mechanisms in the context of pricing and replenishment decisions.
2.2.2
Revenue and Profit Sharing contracts
A revenue sharing contract mechanism involves two parameters, namely W (the
wholesale price per unit) and a percentage J of the retailer’s revenue that goes to the
manufacturer (0< J <1).
Dana & Spier (2001) show that revenue sharing is valuable in vertically separated
industries where the demand is either stochastic (unpredictable) or variable (e.g.,
systematically declining). Downstream inventory is chosen before demand is realized,
and the downstream firms engage in inter-brand competition. They conclude that revenue
sharing achieves a coordinated outcome by softening retail price competition without
distorting the retailer’s inventory decisions. However, their study focuses more on
coordination and does not clearly address the existence of win-win situations.
Pasternack (2001) consider a single inventory (newsvendor) problem in which the Buyer
has a limited amount of funds to purchase items. He assumes that the Supplier will either
sell the items to the Buyer outright or offer the items on a revenue sharing (consignment)
basis. With the consignment contract, the Supplier decides the retail price and delivery
quantity, and retains ownership of the goods. The wholesale price per unit is lower with a
consignment contract, but the Buyer must share some of the revenue with the Supplier.
He investigates which of the circumstances under each of the above contracts would be
beneficial to the Buyer.
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LITERATURE REVIEW
33
Similar to Pasternack (2001), Wang et al. (2004) also consider a consignment contract
with revenue sharing. They show that under a consignment contract both the overall
channel performance and the performance of the individual firms depend critically on
demand price elasticity and on the retailer’s share of the channel cost. In particular, the
(expected) channel profit loss, compared with that of a centralized system, increases with
demand price elasticity and decreases with an increase in the retailer’s share of the cost.
Gerchak & Whang (2004) analyze the applicability of the revenue sharing contract in an
assembly environment. The firm assembling the final product chooses the allocation of
sales revenue among herself and multiple suppliers’ who produce different components
needed for the final product. The firm determines the revenue sharing percentage and the
production quantities. The Suppliers’ then decide on their individual component
production quantities. In a similar assembly setting, Wang & Gerchak (2003) examine
production capacities rather than production quantities. In both the above papers, the
retail price of the final product is considered as an exogenous variable.
Van der Veen & Venugopal (2005) model a video rental supply chain to study pricing
and replenishment decision making. They consider a linearly decreasing rental demand
setting and illustrate that a revenue sharing contract can optimize the chain and provide
win-win situations to the players in the industry.
Cachon & Lariviere (2005) study the revenue-sharing contract extensively in more
generalized settings. They look at the ability of this contract to improve the overall supply
chain performance. They also compare the revenue sharing contract to the buy-back and
quantity flexibility contracts. They show that only revenue sharing can coordinate
systems with a traditional newsvendor setting with price-dependent demand. They also
show that revenue sharing can coordinate systems with multiple competing retailers. In
another study, Koulamas (2006) considers a standard newsvendor problem in a single
manufacturer–retailer channel. This study shows that the conditions for win-win
situations are dependent on the demand distribution.
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Overall, very few studies address the profit sharing mechanism. One study is by Jeuland
& Shugan (1983), who design the profit sharing mechanism in a deterministic setting.
They obtain conditions under which channel coordination can be achieved with the profit
sharing mechanism. Van der Veen & Venugopal (2001) design the profit sharing
mechanism to test its effectiveness for coordination and win-win in a setting where the
end-consumer demand is uncertain. They obtain conditions for both coordination and
win-win opportunities. For details on other studies using profit sharing contracts, we refer
to an extensive review of the literature provided by Tsay et al. (1998).
In the next subsection, we review the literature related to quantity discounts and the
license fee mechanism in the context of pricing and replenishment decisions.
2.2.3 Quantity discounts & the License fee mechanism
A manufacturer who offers the retailer a quantity discount varies the price charged to the
retailer according to the quantity purchased by the retailer. The retailer obtains a discount
for purchasing a larger quantity of the product from the manufacturer. The larger the
quantity purchased, the lower the cost per unit for the retailer.
Jeuland & Shugan (1983) design a quantity discount mechanism for a two member
channel facing deterministic market demand. They demonstrate that if designed correctly,
the quantity discount scheme can coordinate the channel and also share the efficiency
gains between the two players.
Monahan (1984) models a Supplier who follows a lot-for-lot policy and provides quantity
discounts to his Buyer. It is shown that a sufficient discount can induce the Buyer to order
a quantity that would increase the Supplier’s net profit. Interestingly, this modified
quantity is related to the Buyer’s original economic order quantity by a factor that
depends on the ratio of the fixed ordering costs of the two parties. Rosenblatt & Lee
(1985) show that a linear discount schedule can benefit both the Supplier and the Buyer.
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LITERATURE REVIEW
35
Lee & Rosenblatt (1986) extend Monahan’s model to include the Supplier’s lot sizing
decision by considering the inventory carrying and fixed costs incurred by the Supplier.
Bannerjee (1986) takes the perspective of a central decision maker who can jointly
optimize the total costs of both the parties. The author demonstrates that the joint
economic lot-size and the optimal quantity discount schedule benefit both Buyer and the
Supplier. All the above studies design quantity discounts in a setting where the demand is
deterministic.
Moorthy (1987) argues that a wide variety of pricing schemes with quantity surcharges
can coordinate the channel settings considered by Jeuland & Shugan (1983). He
concludes that a two-part tariff is the best in the setting considered by Jeuland & Shugan
(1983).
Weng (1995) extends the work of Jeuland & Shugan (1983). Under the assumption that
the Buyer will receive a fixed fraction of the incremental profit, and shows that a quantity
discount for the Buyer along with a franchise fee paid to the Supplier is sufficient to
induce the Buyer to make decisions that lead to joint profit maximization. Further, the
author shows that the form of the quantity discount scheme (all units vs. incremental
quantity discount) is not critical to achieve channel coordination. The dependence of
customer demand on price and of operating costs on order quantity are the critical factors
to achieve channel coordination.
Ingene & Parry (1995) focus on the issue of channel coordination in a setting where the
manufacturer sells through competing identical retailers. They show that no single twopart tariff with a constant per-unit charge can coordinate the channel. They derive
conditions under which a manufacturer will prefer to offer various two-part tariffs with
constant per-unit charges instead of the channel-coordinating quantity-discount schedule.
Ingene & Parry (2000) suggest a sophisticated Stackelberg two-part tariff for a setting
with competing retailers. Although such a tariff cannot coordinate the channel, it is the
best of all possible two-part tariffs from the viewpoint of maximizing manufacturer
profit. The authors show that the optimal policy is dependent on: 1) the retailer fixed
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costs, 2) the relative size of the retailers, and 3) the degree of inter-retailer competition.
They argue that, from the perspective of a manufacturer, channel coordination is often
undesirable compared to utilizing a non-coordinating, sophisticated Stackelberg pricestrategy.
Chen et al. (2001) suggest coordination mechanisms for a distribution system with one
Supplier and multiple non-identical retailers whose demand is a decreasing function of
the retail price. The traditional discounting scheme, which is based on order quantities
only, does not suffice to optimize channel-wide profits when there are multiple nonidentical retailers. They have shown that coordination can be achieved via periodically
charged fixed fees and non-traditional discount pricing. The discount given to a retailer is
the sum of three discount components based on the retailer’s “annual sales volume,”
“order quantity,” and “order frequency,” respectively.
Raju & Zhang (2005) develop a channel model in which the deterministic demand is
influenced by the price, and the service-level is fixed by the dominant retailer. The
dominant retailer is the one who has a major share of demand and his actions with respect
to price and service levels are of utmost importance to the manufacturer. They show that
such a channel can be coordinated to the benefit of the manufacturer through either
quantity discounts or a menu of two-part tariffs. They caution the manufacturers to
choose the mechanism judiciously, as both mechanisms are not equally efficient from the
manufacturer’s perspective as channel coordinating mechanisms.
Burnetas et al. (2007) investigate how a Supplier can use a quantity discount schedule to
influence the stocking decisions of a Buyer who faces a single period of stochastic
demand. In contrast to much of the work that has been done on single-period supply
contracts, the authors assume that the Buyer has better information about the distribution
of demand than the Supplier. They show that the Supplier can earn larger profits with an
all-unit discount compared to an incremental discount.
In the next subsection, we review the literature on buy-back (return policies) in the
context of pricing and replenishment decisions.
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LITERATURE REVIEW
2.2.4
37
Buy-back (Return policies)
A buy-back (return policies) contract involves three parameters (W, S,U), with W being
the wholesale price per unit, S being a pay-back price ( 0 S d W ) , and U being the
maximum return percentage (0 U d 1) . Under such a contract, the manufacturer sells Q
units to a retailer at W per unit and allows the retailer to return a maximum of UQ items at
the end of selling season for S per unit. If S = W, the contract is said to be a full refund
contract. If U =1, the contract is said to be a full return contract, in which case the retailer
can return all the unsold items at the end of the season. If U <1, the contract is said to be a
partial return contract, in which case the retailer can only return a limited number of the
unsold items (maximum of UQ items) to the manufacturer.
Pasternack (1985) performed the seminal work regarding buyback contracts from a
coordination perspective. He considered a setting in which a manufacturer produces a
short shelf life product, and the retailer places only one order with the manufacturer. He
concludes that full returns at a partial refund can coordinate the channel and that channelcoordinating prices are “independent of the market demand distribution.” This is
significant in that the manufacturer need not know the market demand distribution in
order to implement an efficient contract, although this remains necessary in order to
properly value and allocate efficiency gains. However, the study does not address the
issue of providing win-win conditions explicitly, which is necessary for interorganizational collaboration. This study has led to a host of other studies which analyze
buy-back contracts under different supply chain settings.
Marvel & Peck (1995) study claims that the manufacturer’s decision to accept returns
depends on the nature of the demand uncertainty. Their analysis claims that the
uncertainty over customer arrivals favors returns, while uncertainty over the consumer’s
valuation of the manufacturer’s product leads distributors to set retail prices too high
(from the manufacturer’s standpoint) when returns are allowed.
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Kandel (1996) studies the effectiveness of the buyback contract in a setting where the
end-consumer demand is price sensitive and downward sloping. His study proposes a
consignment contract (full returns for full credit) when the manufacturer can fix the final
selling price and demonstrate coordination. The fixing of the final selling price by the
manufacturer is called resale price maintenance. Emmons & Gilbert (1998) generalize
Pasternack (1985) in much the same way as Kandel (1996); however they assume a
specific multiplicative form of demand model. They show that for a given wholesale
price, the buy-back contract tends to increase the total profits of the channel.
Padmanabhan & Png (1997) bring out the effectiveness of the buy-back contract in a
setting where symmetric retailers compete with deterministic demand. The authors claim
that in such a setting a returns policy subtly induces retailers to compete more intensely.
The provisions of a returns policy reduce retail prices without affecting wholesale prices,
thereby reducing retailer margins and improving the manufacturers’ profitability. Each
retailer will order enough stocks so that it will not be constrained by stocks, thereby
intensifying retail competition. They further consider a general setting in which
competing retailers face uncertain demand and the manufacturer faces a trade-off
between the benefits (more intense retail competition) and the costs (excessive stocking)
of a returns policy. They discover that a manufacturer should accept returns when the
marginal production cost is sufficiently low and the demand uncertainty is not too great.
Donohue (2000) studied a buy-back contract for a two-stage SC in two different settings.
In the first, the Supplier offers the product for delivery at two different lead times. The
Buyer commits in advance to a quantity of the long-lead time item at a given wholesale
price. After revising his demand forecast prior to the season, the Buyer can place an
additional order for a short lead-time delivery at a different wholesale price. At the end of
the season, the manufacturer takes back any unsold items at a third price. The author first
finds that the Buyer’s optimal ordering policy has an order up to structure, and later
determines the three price parameters that will result in the same system profit as in the
optimal centralized solution. A similar analysis is performed for the second setting, an
assemble-to-order setting. Coordination in the first setting entails a type of minimum
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LITERATURE REVIEW
39
purchase commitment in the initial purchase; coordination in the second setting entails an
option-like arrangement which communicates a maximum purchase commitment. As in
Pasternack (1985), the prices that coordinate the channel turn out to be independent of the
distribution of market demand. The author also discusses the method of splitting the
efficiency gains between the Buyer and the manufacturer.
Webster & Weng (2000) design a risk-free returns policy for the manufacturer, which
satisfies the following two conditions when compared to the no returns policy: (1) the
retailer’s expected profit is increased, and (2) the manufacturer’s profit is at least as large
as when no returns are allowed.
Tsay (2001) studies a manufacturer-retailer channel facing uncertain demand. His study
brings out the differences between buy-back and markdown policies and determines the
conditions under which each will be more desirable with respect to channel coordination
and individual firm performance. He concludes that markdown policies can be more
efficient than returns policies, especially when the costs of product handling and returns
are very high. His analysis also proves that markdown policies coordinate the channel
when returns policies cannot. He finally concludes that the markdown policies are not
only in the best interest of the retailer but also help the manufacturer achieve higher
expected profits.
Krishnan et al. (2004) address the inability of buy-back contracts to coordinate due to the
reduced retailer’s promotional effort. They show that while buy-back contracts alone
cannot coordinate the channel, coupling buy-back contracts with promotional cost sharing
agreements (if effort cost is observable), offering unilateral markdown allowances ex post
(if demand is observable but not verifiable), or placing additional constraints on the buyback (if demand is observable and verifiable) does result in coordination. They conclude
that coordinating contracts become more problematic if, for example, the retailer also
stocks substitutes for the manufacturer’s product.
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Yao et al. (2005) investigate the impact of providing a return policy for unsold goods to
two competing retailers facing uncertain demand. Adopting the classic newsvendor
problem model framework and using numerical study methods, the study finds that the
provision of a returns policy is dependent on the market conditions faced by the retailers.
They also analyze the impact of demand variability on the decisions of optimal retail
price, order quantity, and profit reallocation among the manufacturer and the retailers.
Finally, they investigate how the competition factor influences the decision-making of
supply chain members.
Wang et al. (2007) consider the problem of designing a return policy in a supply chain
from a Supplier's perspective. They consider a two-echelon supply chain with one
Supplier and one retailer serving random demand for a short life cycle product. The
retailer can return all the unsold products to the Supplier with a partial refund. They show
that if the retailer orders the optimal quantity to maximize its expected profit, then both
the retailer and the Supplier could benefit from the returns policy. They have also
established that the optimal buy-back price is independent of the mean of the random
demand, but that the variance of the demand has a significant impact on setting the
optimal buy-back price. The higher the variance is, the higher the optimal buy-back price
and the larger the gains in profit of both parties.
Table 2.3 presents the contract literature on the dimension of the pricing and the
replenishment decisions. In Table 2.4 we present the above reviewed literature on the
dimensions of demand and cost characteristics.
Almost all the studies that we have reviewed in the previous subsections have addressed
contracts in different SC settings from the perspective of coordination. Most of the
studies have not addressed win-win opportunities explicitly. In this study, we try to
address the win-win opportunity aspect very explicitly. We also try to address multiple
contracts and discuss the similarities/differences and equivalence very explicitly.
Wherever possible, we also discuss different contract mechanisms from an
implementation perspective.
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Buy-back contract
Ingene & Parry (1995); Ingene &
Parry (2000); Chen et al. (2001);
Van der Veen & Venugopal (2001);
Burnetas et al. (2007)
Pasternack (1985); Marvel & Peck
(1995); Kandel (1996); Emmons &
Gilbert (1998); Donohue (2000);
Webster & Weng (2000); Tsay
(2001); Van der Veen & Venugopal
(2001);Krishnan et al. (2004); Yao et
al. (2005); Wang et al. (2007)
Padmanabhan & Png (1997)
Van der Veen & Venugopal (2001)
Dana & Spier (2001); Pasternack
(2001); Wang et al. (2004); Gerchak
& Wang (2004); Wang & Gerchak
(2003); Cachon & Lariviere (2005);
Koulamas (2006)
Anupindi & Bassok (1999);
Lariviere & Porteus (2001); Cho &
Gerchak (2001); Dong & Rudi
(2001); Bernstein et al. (2002)
Stochastic demand
Jeuland & Shugan (1983);
Monahan (1984); Rosenblatt &
Lee (1985); Rosenblatt (1986);
Bannerjee (1986);Moorthy
(1987); Weng (1995); Raju &
Zhang (2005)
Jeuland & Shugan (1983).
Van der Veen & Venugopal
(2005)
Spengler (1950); Hirshleifler
(1956); Ronen &McKinney
(1970); Gerstner & Hess (1991);
Van der Veen & Venugopal
(2000)
Deterministic demand
Hirshleifler (1956);
Ronen &McKinney
(1970); Cho & Gerchak
(2001); Bernstein et al.
(2002)
Variable marginal cost
Table 2.4: Positioning the pricing and the replenishment literature on dimensions of
demand and cost characteristics
Quantity discount
mechanism/License fee
mechanism
Profit sharing
Revenue sharing
Wholesale price contract
Demand and cost
characteristics/Terms of
trade
Gerstner & Hess
(1991)
Segmented
Consumer
demand
LITERATURE REVIEW
41
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42
2.3
CHAPTER
2
Promotional mechanisms for coordinated decisions in Supply Chains
Sales promotion, a key ingredient in many marketing campaigns, consists of a diverse
collection of incentive tools, mostly short-term, designed to stimulate demand. Sales
promotion includes tools for consumer promotion (samples, coupons, cash refund offers,
prices off, premiums, prizes, patronage rewards, free trials, warranties, tie-in promotions,
cross-promotions, point-of-purchase displays, and demonstrations) and trade promotion
(prices off, advertising and display allowances, and free goods). Since the early 1970s,
price promotions have emerged as an important part of the marketing mix. Increasingly,
they represent the main share of the marketing budget for most consumer packaged
goods. The manufacturer can choose to offer promotions to the retailer believing that he
will pass on some of these benefits to the end-consumer. Such types of promotions are
called trade promotions. When the retailer passes the discount to the end-consumer, it is
called a consumer rebate. The manufacturer can also choose to offer the discount directly
to the end-consumer. This rebate mechanism is called a direct rebate mechanism. The
foremost objective of coordinating any rebate mechanism is to make sure that the total
profit in a supply chain is optimized (coordination) by making sure that all the players
including the consumers benefit (win-win). Figure 2.1 represents different rebate
mechanisms used in supply chains.
promotion
TradeTrade
promotion
Supplier Supplier
Buyer
Buyer
Direct rebate
Direct rebate
Consumer rebate
End consumer
End consumer
Consumer rebate
Figure 2.1: Types of rebate mechanisms in supply chains
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LITERATURE REVIEW
In this section, we provide a brief review of the promotional mechanisms for SC
coordination. Table 2.5 provides an overview of the studies that have used different
promotions mechanisms for coordination.
Decision /
Terms of trade
Pricing and
Replenishment
Promotion
Quality of
Service
Product line
decision
Kumar et al. (2001); Taylor (2002);
Arcelus & Srinivasan (2003)
Trade
promotions
Consumer
rebates
Zhang et al. (2000); Huchzermeier et
al. (2002)
Direct rebates
Gerstner & Hess (1991); Gerstner &
Hess (1995); Nevo & Wolfram
(2002); Arcelus & Srinivasan (2003);
McGuiness (2003); Anderson &
Song (2004); Arcelus et al. (2005)
Table 2.5: Promotional mechanisms for SC coordination
In each of the next subsections, we provide a summary of the literature on promotions
mechanisms from coordination and win-win perspectives. We outline the relevance of
each study and highlight limitations wherever possible.
2.3.1
Trade Promotions
Kumar et al. (2001) examine the strategic considerations that underlie a retailer’s decision
to pass through (i.e., the retailer passing on the trade-deal to the end-consumer) a tradedeal. In particular, their study answers the following questions: (i) What and how do
product-market characteristics impact the extent of retail opportunism? (ii) How can the
manufacturer alleviate the retail pass through problem by strategically supplementing
trade promotions with advertising trade deals directly to consumers? Their study does not
address the issue of providing coordination and win-win opportunities directly but
focuses more on improving the effectiveness of trade promotions.
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Taylor (2002) demonstrates the superiority of a target rebate (a rebate that is provided for
those items that are sold beyond a predefined set threshold) over a linear rebate (a rebate
that is provided for all the units sold) in achieving coordination and win-win. His study
concludes that when the demand is not influenced by the sales effort, a properly designed
target rebate achieves channel coordination and a win-win outcome. When the demand is
influenced by the retailer’s sales effort, a properly designed target rebate and buy-back
contract achieves coordination and a win-win outcome. Contrary to the view expressed in
the literature, the author finds that accepting returns strengthens the incentive for retailer
sales effort.
Arcelus & Srinivasan (2003) evaluate the role of trade incentives specifically designed to
prevent the retailer’s forward-buying practices by examining the use of scan backs and
direct rebates. This study analyzes the link between the retailer’s pricing policy and the
discount policy using scanner data. The authors’ also analyze the economic effectiveness
of pull discounts (which are offered directly to end-consumers). The economic effects of
these incentives are evaluated in terms of their effect on the performance of supply chain
players.
In the next subsection, we review the literature related to consumer rebates.
2.3.2
Consumer rebates
Retailers use consumer rebates in the form of coupons (direct-mail, free-standing inserts,
on-pack, peel-off, in-pack), premiums, rebates, contests, and prize packs to attract
consumers. Peel-off coupons, direct mail coupons and price packs provide consumers
with an immediate benefit upon purchase. This form of rebates can be referred to as
front-loaded incentives. However, in-pack coupons, on-pack coupons, contests, and
loyalty programs require repeat brand purchases and reward the consumer on a future
purchase occasions. This form of rebates can be referred to as rear-loaded incentives.
Zhang et al. (2000) analyze the applicability of different incentive programs in consumer
markets. Their analysis shows that the innate choice process of consumers (variety-
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LITERATURE REVIEW
45
seeking or inertia) is an important determinant of the relative impact of front-loaded or
rear-loaded incentives. They show that in markets with high variety-seeking customers it
is more profitable for a firm to rear-load, while in markets with high inertia it is more
profitable to front-load.
Huchzermeier et al. (2002) build a demand model in which consumers react intelligently
to retail promotions through stockpiling and package size switching. Their analysis shows
the impact of price promotions on reduced inventory costs. Data from the German
grocery industry is used for an empirical fitting of the model.
In the next subsection, we review the literature related to direct rebates.
2.3.3 Direct Rebates
Gerstner & Hess (1991) have looked at the effectiveness of different channel price
promotions in a setting where the market is made up of two different consumer segments:
high willingness-to-pay consumers and low willingness-to-pay consumers. Their study
reveals an important fact that the manufacturer can stimulate sales by a temporary
wholesale price reduction for the retailer, a rebate directed towards consumers, or a
combination of both. They analyze the trade-offs between these promotions and provide
insights about their roles, profitability, and welfare properties. Gerstner and Hess (1995)
propose the pull promotions as a coordination device in the same setting as in Gerstner &
Hess (1991). They show that manufacturers can enhance channel price coordination by
designing pull price discounts that target price-conscious consumers. They advocate the
combination of push and pull to increase the chance of achieving coordination.
Arcelus et al. (2005) test the effectiveness of different rebate mechanisms. They consider
a joint development of the optimal pricing and ordering policies of a profit-maximizing
retailer faced with (i) a manufacturer trade incentive in the form of a price discount or a
rebate directly to the end-consumer, (ii) a stochastic consumer demand dependent on the
selling price and of the trade incentive, and (iii) a single-period newsvendor-type setting.
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They clearly show that, as compared to the no-risk demand, dealing with stochastic
demand leads to (i) (lower) higher retail prices if additive (multiplicative) error, (ii) lower
(higher) pass through if additive (multiplicative) error, (iii) higher claw backs, and (iv)
higher rebates to achieve equivalent profits.
Other studies which have addressed direct rebates are Nevo & Wolfram (2002), Anderson
& Song (2004), Arcelus & Srinivasan (2003) and McGuiness (2003).
Table 2.5 presents the literature on contract mechanisms on the dimension of the
promotional decisions. In Table 2.6 we present the above reviewed literature on other
dimensions like the demand and cost characteristics.
In the next section, we address the coordination literature related to the quality or servicelevel.
Demand and
cost
characteristics/
Terms of trade
Trade promotions
Consumer rebates
Direct rebates
Deterministi
c demand
Stochastic demand
Kumar et al. (2001); Taylor
(2002); Arcelus & Srinivasan
(2003)
Zhang et al. (2000);
Huchzermeier et al. (2002)
Gerstner & Hess (1991);
Gerstner & Hess (1995); Nevo
& Wolfram (2002); Arcelus &
Srinivasan (2003); McGuiness
(2003); Anderson & Song
(2004); Arcelus et al. (2005)
Segmented
consumer
demand
Variable
marginal cost
Gerstner &
Hess (1991)
Combined rebate
mechanism
Table 2.6: Positioning the promotions literature on dimensions of
demand and costs characteristics
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LITERATURE REVIEW
2.4
47
Coordinating the Service (Quality) decisions in Supply Chains
The demand for a product is not only influenced by price and promotions, but also by the
quality of the product and the service-level provided at the retail outlet. Good product
quality and a high service-level provided can have a positive impact on demand. A good
quality product will also reduce the total supply chain costs to a very great extent. In
essence high quality and a high level of service will provide a double advantage by
increasing the demand and reducing the total costs. It is because of the above reason that
maintaining an optimal level of quality or service-level can be critical to the success of
the SC.
A retailer can increase a product’s demand by lowering the product’s price. He can
alternatively take other actions to spur demand: hire more salespeople, improve their
training, increase advertising, better maintain the attractiveness of the product’s display,
enhance the ambience of the store interior (e.g., richer materials, wider aisles) and give
the product a better stocking location within the store. All of these activities are costly.
As a result, a conflict exists between the Supplier (manufacturer) and the retailer; no
matter what level of effort the retailer dedicates towards those activities, the Supplier
prefers that the retailer exert even more effort. The problem is that those activities benefit
both firms but are costly to only one. Because of the above reason, an optimal level of
service at the retail outlet is rarely provided.
Sharing the cost of effort is one solution to the coordination problem. For example, the
Supplier could pay some of the retailer’s advertising expenses, or she could compensate
the retailer for a portion of his training cost. Several conditions are needed for cost
sharing to be an effective strategy: the Supplier must be able to observe (without much
hassle) that the retailer actually engages in costly activity (so the Supplier knows how
much to compensate to the retailer). The Supplier generally can observe and verify
whether or not a retailer purchased advertising in a local newspaper. Furthermore, if the
ad primarily features the Supplier’s product, then the benefit of the ad is directed
primarily at the Supplier. There are also many situations in which cost sharing is not
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2
effective for the Supplier, such as when an advertisement merely promotes the retailer’s
brand image and enhances the demand for all of the retailer’s products and not just the
Supplier’s product. Also, there are many demand-improving activities that are too costly
for the Supplier to observe.
In this section, we provide a review of the mechanisms for coordinating quality or
service-level decisions. Table 2.7 provides an overview of the studies that have addressed
the issue of quality or service-level in the context of SC coordination.
Decision / Terms of
trade
Pricing and
Replenishment
Promotion
Quality of Service
Wholesale price
contract + effort
costs or failure costs
Chu & Desai (1995); Netessine
& Rudi (2000); Gilbert & Cvsa
(2000); Wang & Gerchak
(2001)
Revenue sharing (or)
Royalty payment
Lal (1990); Reyniers & Tapiero
(1995); Baimen et al. (2000);
Startbird (2001); Baimen et al.
(2001)
Quantity discount &
License fee
Raju & Zhang (2005)
Product line
decision
Table 2.7: Mechanisms for coordinating quality and service-level decisions
We provide a summary of the literature on quality or service-level decisions. Most of the
literature on coordinating quality and service-level decisions uses a wholesale price
contract or a wholesale price with the new dimension of effort cost or cost of failure. We
discuss the contributions of each study and highlight the limitations wherever possible.
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LITERATURE REVIEW
49
2.4.1 Wholesale price contract + Cost sharing
Chu & Desai (1995) study a model where the Supplier can also exert costly effort to
increase demand, e.g., brand building advertising, but the impact of effort occurs with a
lag: They have a two-period model and effort in first period increases demand only in
second period. They expand the retailer’s effort model to include two types of efforts: (1)
an effort to increase short-term (i.e., current period) sales; and (2) long-term effort to
increase long-term customer satisfaction and demand (i.e., second period sales). They
assume that the Supplier compensates the retailer by paying a portion of his effort cost
and/or by paying the retailer based on the outcome of his efforts, i.e., a bonus for high
customer satisfaction scores. The issue is to decide the approximate mix between the two
types of compensation.
Gilbert & Cvsa (2000) study a model with costly effort that is observable but not
verifiable, i.e., the firms in the SC can observe the amount of effort taken, but the amount
of effort taken is not verifiable to the courts, and therefore not contractible. In their
model, the Supplier sets a wholesale price and the Buyer can invest to reduce his
marginal cost. The investment to reduce the marginal cost is observed by both firms even
before the Supplier chooses the wholesale price. The Buyer cannot fully capture the
benefit of cost reduction because the Supplier will adjust her wholesale price based on the
observed effort. Hence, the Buyer invests less in the effort to reduce cost than is optimal.
The Supplier can do better if the Supplier commits to a wholesale price before observing
the Buyer’s cost reduction. However, random demand makes it beneficial to choose the
wholesale price after observing demand, which is a conflict. The authors’ demonstrate
that a hybrid solution works well: the Supplier commits to a wholesale price ceiling
before observing the Buyer’s effort and the demand realization, and after the observations
the Supplier chooses a wholesale price that is not greater than her wholesale price ceiling.
Therefore, there is partial wholesale-price commitment and partial flexibility.
Netessine & Rudi (2000) present a coordinating contract which involves sharing
advertising costs. In their model, the Supplier shares a part of the retailer’s expenditure
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for advertising the Supplier’s brand, thus increasing the demand for the product. In Wang
& Gerchak (2001), the retailer’s shelf space can be considered an effort variable. They
also allow the Supplier to compensate the retailer for his effort, which in their model
takes the form of an inventory subsidy.
2.4.2
Revenue sharing/Royalty payments
Lal (1990) also includes Supplier effort, but the effort again is not enforceable. Although
revenue sharing (in the form of royalty payments) continues to distort the retailer’s effort
decision, it provides a useful incentive for the Supplier to exert effort: the Supplier will
not exert effort if the Supplier’s profit does not depend directly on retail sales. Lal (1990)
also considers a model with multiple retailers and horizontal spillovers, that is to say, the
demand-enhancing effort at one retailer may increase the demand at other retailers. These
spillovers can lead to free riding, i.e., one retailer enjoys higher demand due to the efforts
of others without exerting his own effort. The author suggests that the franchisor can
control the problem of free riding by exerting a costly monitoring effort and penalizing
franchisees that fail to exert sufficient effort. Cachon (2006) provides a review of the
literature on coordinating the newsvendor model with effort dependent demand.
Several papers study the impact of efforts exerted by SC players on quality. In Reyniers
& Tapiero (1995) there is one Supplier and one Buyer. The Supplier can choose between
two production processes, one that is costly but produces high quality products (in the
form of low-defect probability) and one that is inexpensive but produces low quality
products (a high-defect probability). The choice of production process can be taken as a
proxy for effort in this model. The Buyer can test each unit the Supplier delivers, but
testing is costly. Defective units that are discovered via testing are repaired for an
additional cost incurred by the Supplier, i.e., an internal failure cost. If the Buyer does not
test and the unit is defective, then an external failure cost is incurred by the Buyer. The
authors’ allow a contract that includes a wholesale-price rebate for internal failures and
external failure compensation, i.e., the Supplier pays the Buyer a portion of the Buyer’s
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51
external failure cost. Internal failures are less costly to the Supplier (repair cost plus
rebate cost) than external failures (compensation to the Buyer), so the Supplier benefits if
the Buyer tests a higher fraction of units.
In Baimen et al. (2000), the Supplier can exert costly effort to improve quality and the
Buyer exerts a testing effort that yields an imperfect signal of quality. Both effort levels
are continuous variables, as opposed to discrete effort levels as in Reyniers & Tapiero
(1995). If testing suggests the product is defective, the Buyer incurs an internal failure
cost. If testing suggests the product is not defective (and hence the Buyer accepts the
product), then an external failure cost is incurred if the product is in fact defective. They
show that optimal SC performance is achievable when both effort levels are contractible.
Optimal performance is also possible if the firms can verify the external and internal
failures and therefore commit to transfer payments based on those failures.
Starbird (2001) proposes that rewards for better quality, penalties for poorer quality, and
the type of inspection policy are among the most common quality-related provisions of
supply chain contracts. He examines the effect of rewards, penalties, and inspection
policies on the behavior of a Supplier who is expected to minimize cost. He assumes that
the Supplier selects a batch size and target quality level in order to meet a Buyer’s
deterministic demand. He shows that the reward and/or penalty that motivate a Supplier
to deliver the Buyer’s target quality depend upon the inspection policy. He concludes that
when sampling inspection is used, there exists a unique reward/penalty combination at
which the Buyer’s expected cost of quality is zero.
Baiman et al. (2001) extend their model to include the issue of product architecture. With
modular design the firms can attribute external failures to a particular firm: either the
Supplier made a defective component, or the Supplier made a good component but the
Buyer caused a defect by poor handling or assembly. However, with an integrated design
it is not possible to attribute blame for a product’s failure. Hence, the product architecture
influences the contract design and SC performance.
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2.4.3
2
Quantity discounts and Two-part tariff contracts
Raju & Zhang (2005) develop a channel model in which the deterministic demand is
influenced by the price and the service-level fixed by the dominant retailer. They show
that such a channel can be coordinated to the benefit of the manufacturer through either
quantity discounts or a menu of two-part tariffs.
Table 2.7 presents the literature on contract mechanisms on the dimension of quality or
service-level. In Table 2.8 we present the above reviewed literature on other dimensions
like the demand and cost characteristics.
Demand and cost
characteristics/
Terms of trade
Wholesale price
contract + effort costs
or failure costs
Deterministic
demand
Chu & Desai (1995)
Variable
marginal cost
Segmented
consumer
demand
Netessine & Rudi
(2000); Gilbert & Cvsa
(2000); Wang &
Gerchak (2001)
Lal (1990); Reyniers &
Tapiero (1995); Baimen
et al. (2000); Startbird
(2001); Baimen et al.
(2001)
Revenue sharing (or)
Royalty payment
Quantity discount &
License fee
Stochastic demand
Raju & Zhang
(2005)
Table 2.8: Positioning the quality or service-level literature on the dimensions
of demand and costs characteristics
In the next section, we review the literature related to the coordination of product-line
decisions.
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2.5
53
Coordinating product-line decisions in Supply Chains
When designing a product line, a manufacturer is often aware that he does not control the
ultimate targeting of the products to different consumer segments. While the
manufacturer can attempt to influence the target customers through communications in
appropriate media, appropriate product design, and the choice of channels of distribution,
the ultimate targeting is made by a retailer. The retailer may in turn only care about his
own interests, and is fully in control of interactions with customers, including how the
product is sold and displayed. This occurrence is widespread in numerous markets such
as frequently purchased consumer products, home appliances, personal computers,
automobiles, et cetera. The resulting tension of selling a product line through a dealer
(distributor) is well documented in the automobile industry, see, e.g., Villas-Boas (1998).
Dealers and manufacturers negotiate and decide the appropriate mix of products (which
reflect the appropriate targeting) that should be carried by the dealers. The dealers want to
carry the “fast-selling” automobiles and drop the “hard-to-market” models. These
classifications obviously depend on the dealer’s intended targeting strategies. For
example, in Maxfield v. AMC (1981) it is noted that AMC may have forced the dealer
(Maxfield) to carry the large “hard-to-market” cars (Ambassadors and Matadors) in
return for carrying the small “fast-selling” models (Gremlins & Hornets), see e.g., VillasBoas (1998).
Product line decisions have mostly focused on the selection of the optimal assortment for
retailers which will minimize their inventory and obsolescence costs. In this literature
study, we will discuss the product line literature which addresses the issue of channel
coordination. Table 2.9 provides an overview of the studies that have addressed the issue
of product-line decisions.
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CHAPTER
Decision/Terms of
trade
Pricing
and
Replenishment
Promotion
Quality
of
Service
2
Product line decision
Wholesale price contract
Hotelling (1929); Mussa & Rosen
(1978); Moorthy (1984); Dobson &
Kalish (1993); De Groote (1994);
Chen et al. (1998); Downs et al.
(2002); Mcgillivray & Silver (1978);
Parlar & Goyal (1984); Noonan
(1995); Lancaster (1990); Rajaram &
Tang (2001); Netessine & Rudi
(2003); Parlar (1985); Villas-Boas
(1998); van Ryzin & Mahajan (1999);
Singh et al. (2005); Cachon & Kok
(2006)
Revenue sharing + profit
sharing + license fee+
buy-back contract+
quantity discount
contract
Singh et al. (2005)
Table 2.9: Mechanisms for coordinating product line decisions
We provide a summary of the literature on product line decisions. Most of the literature
on product line decisions, with the exception of Singh et al. (2005), uses the wholesale
price contract. We discuss the relevance of each study and highlight the limitations
wherever possible.
Pioneering efforts in the product line decision literature are due to Hotelling (1929),
Mussa & Rosen (1978), McGillivray & Silver (1978), Moorthy (1984), Parlar and Goyal
(1984). Lancaster (1990) provides an excellent review of this literature. Other notable
contributions for product line design are made by Anderson et al. (1992), Dobson &
Kalish (1993), De Groote (1994), Noonan (1995), Chen et al. (1998), Desai et al. (2001),
and Rajaram & Tang (2001). Most of these studies have not approached product line
decisions from a SC perspective, i.e., they do not address the issue of the product line
design problem under the centralized and decentralized management regimes.
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LITERATURE REVIEW
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Villas-Boas (1998) considers a two player SC targeting different products to consumers
with different willingness-to-pay. The author address the issue of coordination of the
product line decision in the above setting, and obtain conditions under which a
decentralized channel stocks lower product variety when compared to the centralized
channel.
Van Ryzin & Mahajan (1999) consider a category of product variants distinguished from
one another by attributes such as color or flavor. They consider the problem of deciding
which variants to stock and how much of each variant to stock. The consumer choice
process is based on the multinomial logit concept. Their analysis provides insights on
how various factors affect the optimal level of assortment variety.
Netessine & Rudi (2003) investigate the n product case under centralized and
decentralized management regimes. They find that more inventories are carried in a
decentralized regime than in the centralized regime because of competition effects. The
complexity of the problem is prohibitive and it is not possible to obtain an explicit
solution to the problem.
Singh et al. (2005) study a simple, price-only contract between a wholesaler and a retailer
in a multi-product setup. They use the Stackelberg game approach in which the
wholesaler sets the wholesale price and the retailer makes quantity and assortment
decisions. For a suitable family of demand distributions, it is shown that the retailer will
construct his optimal assortment by choosing product variants in decreasing order of his
customers’ preference. Subsequently, they focus on the case of normally distributed
demand and study the supply chain efficiency. They show that a lack of coordination in
the channel manifests itself as a smaller assortment offered by the retailer. Finally, they
examine revenue sharing, profit sharing, quantity discounts, buy-back contracts, and
quantity flexibility contracts in a multi-product setup and show that these contracts
coordinate the supply chain in terms of both the optimal assortment and optimal
quantities chosen by the retailer.
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Cachon & Kok (2006) study the assortment planning problem with multiple merchandise
categories. They present a model in which retailers choose the number of variants to offer
in each category and the consumers of multiple categories (i.e., basket shoppers) choose
among retail stores. The authors investigate the interaction of the category variety
decisions at the retail store under centralized and decentralized management regimes. The
common practice of category management is an example of a decentralized regime for
controlling assortment because each category manager is responsible for maximizing his
or her assigned category’s profit. The authors succeed in showing that category
management never provides an optimal solution and generally provides less variety than
is optimal. They also provide guidelines as to which types of categories the retailer
should carry and which ones should have more variety. Kok et al. (2006) review the
coordination literature on assortment planning.
Table 2.9 presents the literature on contract mechanisms on the dimension of product line
decisions. In Table 2.10 we present the above reviewed literature on other dimensions of
demand and cost characteristics.
In the next section, we conclude by providing some insights based on our literature study.
2.6
Conclusions & the relevance of the Chapters 3-9
In this chapter, we have discussed the selected literature on SC coordination with
contracts. Most of the literature has focused on coordinating pricing and replenishment
decisions. Almost all the studies on contracts address the issue of coordination but not
win-win opportunities. Since win-win opportunities are a necessary condition for SC
coordination, we explicitly address the issue of providing win-win opportunities in the
entire thesis. In this dissertation we address almost all the limitations that are identified in
our literature analysis.
More specifically, Chapter 3 of this dissertation was motivated by Van der Veen &
Venugopal (2000). Van der Veen & Venugopal (2000) perform an extensive analysis to
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Hotelling (1929); Mussa & Rosen
(1978); Moorthy (1984); Dobson &
Kalish (1993); De Groote (1994); Chen
et al. (1998); Downs et al. (2002);
Mcgillivray & Silver (1978); Parlar &
Goyal (1984); Noonan (1995); Lancaster
(1990); Rajaram & Tang (2001);
Netessine & Rudi (2003); Parlar (1985);
Villas-Boas (1998)
Deterministic demand
Singh et al. (2005)
van Ryzin & Mahajan
(1999); Singh et al. (2005);
Cachon & Kok (2006)
Stochastic demand
Variable marginal
cost
of demand and cost characteristics
Table 2.10: Positioning the product line decisions literature on dimensions
Revenue sharing + profit sharing +
license fee+ buy-back contract+
quantity discount contract
Wholesale price contract
Supply Chain settings/Terms of
trade
Villas-Boas (1998).
Segmentation of
consumers
LITERATURE REVIEW
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demonstrate the double marginalization phenomena. They have proposed a partnership
scenario under which the above phenomena can be eliminated. In this study we design
contract mechanisms with a focus on both coordination and win-win. We also establish
an equivalence relationship between different contracts and also discuss these contracts
from an implementation perspective.
Chapter 4 was motivated by the classic paper in accounting literature, namely Hirshleifler
(1956), and Ronen & McKinney (1970). These papers designed transfer pricing
mechanisms to coordinate the pricing and the replenishment decisions among different
divisions of the same firm. However, Hirshleifler’s method of transfer pricing does not
provide win-win opportunities. Furthermore, Ronen & McKinney’s method requires
accounting adjustments at the corporate level. Clearly, for the SC where the entities are
independent organizational units, win-win opportunities are necessary and corporate level
accounting adjustments are not possible. Therefore, contract mechanisms with a focus on
both coordination and win-win are designed in this study.
Chapter 5 finds it roots in Gerstner & Hess (1991, 1995). In these papers, a SC model
with two consumer segments, each with their own willingness-to-pay, are introduced. It is
shown in this chapter that the direct rebate mechanism (mail-in-rebate) as suggested by
Gerstner & Hess (1991, 1995), does not coordinate the SC for all parameter values. This
study designs the revenue and profit sharing mechanisms in the above setting.
Chapter 6 is motivated by the seminal work of Pasternack (1985) where the ability of the
buy-back contract from the perspective of coordination was tested. However, Pasternack
(1985) did not address the issue of win-win explicitly. In this study we analyze various
coordination mechanisms such as profit sharing, revenue sharing, two-part tariff (license
fee) and buy-back mechanisms for both coordination and win-win.
The motivation for Chapter 7 has is obtained from the study of Gerstner & Hess (1991).
Gerstner & Hess (1991) have looked at the effectiveness of different channel price
promotions in a setting where the market is made up of two different consumer segments:
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LITERATURE REVIEW
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high willingness-to-pay consumers and low willingness-to-pay consumers. One of the
major results of the study by Gerstner & Hess (1991) is that direct rebates (pull
promotions) and trade promotion (push promotions) does not coordinate the SC for all
parameter values. We consider a SC setting in which the end-consumer demand is price
sensitive and deterministic. Our results concur with that of Gerstner & Hess (1991), as it
is shown that the direct rebates and trade promotion do not provide both coordination and
win-win opportunities. In this study we design a new mechanism the combined rebate
mechanism, and analyze it from the perspective of both coordination and win-win.
The model in Chapter 8 of this dissertation resembles the one discussed in Raju & Zhang
(2005), with the exception that we do not consider the dominant Buyer concept. To the
best of our knowledge, this model has not been studied extensively from the perspective
of coordination of both pricing and service-level decisions. Also, we are not aware of a
study which has explicitly addressed the win-win aspect. Four contract mechanisms,
namely the revenue sharing, profit sharing, quantity discount, and the license fee
mechanisms, are designed in two different settings. In the first setting the Buyer makes
the service-level decision and in the second setting the Supplier makes the service decision.
The study by Villas-Boas (1998) provided the motivation for Chapter 9 of this
dissertation. Villas-Boas (1998) does not address any specific coordination mechanisms.
This motivated us to take up this study to design mechanisms from the perspective of
coordinating product line decisions and providing win-win opportunities. Quite
surprisingly we come to a result in the decentralized scenario which has not been reported
in the literature, namely in a given setting double marginalization could result in stocking
fewer or more variants depending on the parameter values. We perform an extensive
analysis in the decentralized scenario. We analyze the slotting allowance mechanism, in
which lump-sum payments are made by the Supplier to the Buyer. It is shown that the
slotting allowance mechanism does not provide coordination and win-win for all the
parameter values. Furthermore, we design revenue and profit sharing mechanisms and
show that coordination and win-win opportunities are achieved for all parameter values.
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61
Part 1: Contract Mechanisms for Coordinating Pricing
and Replenishment Decisions in a Supply Chain
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63
Chapter 3
Coordinating Pricing and Replenishment Decisions in a Price Senstitive
Deterministic SC 1
Chapter Synopsis
In this chapter, we consider the pricing and replenishment decisions in a two-echelon
supply chain (SC) in which the end-consumer demand is price sensitive and
deterministic. First, it is shown that if the decisions are distributed over the entities in the
SC this leads to a sub-optimal situation. To overcome such difficulties, various contract
mechanisms (revenue sharing, profit sharing, quantity discounts and license fees) are
designed and tested for their ability to provide coordination (the SC optimal result) and
win-win conditions for all entities in the SC. Moreover, an equivalence relationship
between different contract mechanisms is established and the benefits of one mechanism
over another from an implementation perspective are discussed.
3.1
Introduction
For the majority of companies involved in some form of manufacturing or service
delivery, two types of operating decisions are of great importance. One concerns the
pricing of finished products and the other the replenishment of their inputs. Most firms
usually devote a lot of attention to coordinating either the pricing or the replenishment
decisions to improve their profitability. However, such a limited focus often leads to
inefficiency and a lower profitability. In contrast, coordinating these two decisions across
different organizations can improve the profitability of the SC and in turn benefit all the
1
This chapter is a revised, updated and elaborated version of the NRG working paper [Reference: Nalla, V.
R, J.A.A van der Veen, and V. Venugopal (2005)]
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contributing parties in the SC. To achieve this objective, the various firms within the SC
need to coordinate their pricing and replenishment decisions. In this chapter, we intend to
highlight the inefficiencies that can result by not considering decisions jointly and
introduce mechanisms which can coordinate both the pricing and replenishment
decisions. Clearly, the coordinating mechanism is incomplete and cannot be implemented
unless it has the scope to improve each player’s profit (i.e., leads to a win-win situation in
the entire SC). Our objective in this chapter is to design mechanisms which can
coordinate both the pricing and replenishment decisions across firms and distribute the
additional profits among them. Examples given below emphasize the benefits of
coordinating the pricing and the replenishment decisions.
In the 1990’s, Hollywood movie studios such as Universal Studios and Sony Pictures
found that frequent stock-outs at video retailers like Blockbuster and Movie Gallery
posed a major problem. A lack of inventory on store-shelves meant that everyone
suffered: the studios lost potential sales, video rental companies lost income, and
consumers went home disgusted. The reasons for low inventory on store shelves were
high price and the temporal demand pattern of video tapes. In the 1990’s, the studios
(Supplier) and the rental stores (Buyer) jointly decided to solve the problem. In the
process, studios decided to sell tapes for $3 per tape instead of the original price of $65
and agreed to receive 50% of the revenue from each rent. The studios saw a bounce in
their bottom lines, retailers began to earn more money, and consumers no longer went
away disappointed. Industry experts estimated that rental revenues from videotapes
increased by 15% in the United States, and the studios and the retailers enjoyed a 5%,
growth in profits. Perhaps most important, stock-outs at video rental stores fell from 25%
before revenue sharing to less than 5% after revenue sharing, see, Cachon & Lariviere
(2001).
The revenue sharing mechanism came as a boon for outlet renters in the Netherlands. The
outlet renters were comprised of financiers and investors who made large investments in
building huge factory outlet stores and renting them out to individual retailers. Initially,
retailers were reluctant to pay high rental fees charged by the renters because of the
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65
uncertainty in the business environment. This led to a situation in which many stores
were left unrented. At the same time the option of charging lower rent was not profitable
for the renters. This discouraged the renters from building new rental stores until the
renters and retailers jointly decided to solve the above problem by signing a revenue
sharing contract. With the revenue sharing contract mechanism the retailers would pay
the renters a percentage of their revenues in addition to a low fixed rental fee. This way
the risk associated with the business environment was shared between the retailers and
the renters. This new mechanism has suddenly increased the demand for the stores and
the renters have started to plan new investments to build outlets stores in different parts of
the Netherlands (see, Het Financieele Dagblad (2005)).
In this chapter we address the following research questions related to pricing and
replenishment:
x
Which contract mechanisms coordinate the pricing and the replenishment decisions in
a given SC setting?
x
Do all the coordinating mechanisms provide a win-win opportunity to all players?
x
Can we establish an equivalence relationship among different mechanisms which can
coordinate pricing and replenishment decision?
x
Are there any differences among equivalent mechanisms from an implementation
perspective?
In this chapter we consider a SC in which the end-consumer demand is price sensitive
and deterministic. We design different contract mechanisms, namely the revenue sharing,
profit sharing, quantity discount and license fee mechanisms. We test these contract
mechanisms for coordination and win-win opportunities. An equivalence relationship
among the parameters of different contract mechanisms is also established wherever
possible. When an equivalence relationship exists among different contract mechanisms,
we discuss possible benefits of one mechanism over another from an implementation
perspective.
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The remainder of this chapter is organized as follows. In the next section we present the
basic SC model and demonstrate that sub-optimization is inevitable under the standard
contracts. Subsequently, we design different contract mechanisms and establish a
relationship among them. Finally, we conclude the study.
3.2
Model and Basic Analysis
Consider a two-echelon SC with a Buyer and a Supplier. The Supplier sells a product
with a short life cycle (e.g., a fashion product) to the Buyer who resells the product to the
consumers, see Figure 3.1. Both the Supplier and the Buyer are free to set the price they
charge to their customer(s). Both the players have symmetric and perfect information as
to the demand and the cost functions.
Supplier
Buyer
Figure 3.1: A simple SC.
C
O
N
S
U
M
E
R
S
It is assumed that the final customer demand for the product (denoted by D) depends
linearly on the price P per unit set by the Buyer, i.e.,
D( P)
D EP
(3.1)
with D , E ! 0 . Once the Buyer has set the price P, he can observe the demand D and
places an order of size Q
D(P ) with the Supplier. The Supplier is faced with a cost of c
per unit and chargers a wholesale price W per unit to the Buyer. The Buyer does not have
any cost associated with his operation other than the purchasing cost of W per unit. It is
assumed that both players have symmetric and perfect information. Furthermore, to
ensure realistic values, throughout it is assumed that:
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67
0 d c P d DE ; and
(3.2)
c dW d P .
(3.3)
In the above setting, the Supplier can set the wholesale W such that his profit:
S
W c Q
(3.4)
is maximized. The Buyer has information on the final customer demand (i.e., knows
D and E ), and is faced with price W . He can set the price P such that his profit
B
P W Q
(3.5)
is maximized. The SC profit is defined by:
T: SB
P c Q.
(3.6)
We will study the above model under three basic scenarios. First the so-called centralized
scenario is discussed. Under this scenario it is assumed that the Buyer and the Supplier
work together as a single entity with the objective to maximize the SC profit. The second
scenario discussed is the solitaire-scenario. Here firstly the Supplier sets his price W. The
Buyer facing price W and demand function D(P) determines his optimal price P, i.e., the
price that maximises profit B. Then, an order of size Q
D(P ) is placed to the Supplier.
The third scenario considered is called the partnership-scenario. Under this scenario, the
Supplier and Buyer jointly determine P and W . Subsequently, we design different
contract mechanisms and establish a relationship among them.
3.3
The centralized scenario
We start with the centralized scenario (which will be denoted by a subscript 0). Note that
the expression for total SC profit T in Equation (3.6) does not depend on the wholesale
price W, but depends only on the order quantity Q. In other words, from the perspective
of the centralized scenario only the optimal order size for the entire SC is to be
determined. By assuming Q
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D(P) , substituting Equation (3.1) in Equation (3.6) and
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determining the first order relation with respect to P, the SC optimal price can be
obtained as:
D Ec
,
2E
P0* :
(3.7)
hence the optimal order size is given by:
Q0* :
1
2
D Ec .
(3.8)
It follows that the maximal SC profit is given by:
T0
Defining:
–:
D Ec 2
.
(3.9)
D Ec 2 ,
(3.10)
4E
4E
the total SC profit in the centralized scenario is T0
3.4
–.
The solitaire scenario
Assume in the solitaire scenario (denoted by subscript 1) that the Supplier has set a price
W1 . Obviously, the Buyer wants to maximise his profit, i.e., he chooses P1 such that:
B1
P
1
W1 (D EP1 )
E ( P1 ) 2 D EW1 P1 DW1
(3.11)
is maximized. The optimal price is then given by:
D EW1
.
2E
P1 :
(3.12)
It follows from Equation (3.1) that the optimal order size is:
Q1* :
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1
2
D EW .
1
(3.13)
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Assuming the optimal price P1* and order quantity Q1* are used, the following profits can
be derived from Equations (3.4)-(3.6):
·
1 §D 2
B1 W1 : ¨¨
2DW1 EW12 ¸¸
4© E
¹
D EW 2
4E
1
(3.14)
for the Buyer;
S1 W1 :
(3.15)
·
1 §D 2
¨
2Dc 2 E cW1 EW12 ¸¸
4 ¨© E
¹
(3.16)
1
Dc D Ec W1 EW12
2
for the Supplier; and
T1 W1 :
for the SC.
Note that all profits under the solitaire-scenario depend on the Supplier’s price W1 .
Given this fact, the question is: What is the value that the Supplier should choose for
W1 ? Clearly, from Equation (3.3), c d W1 d P1 . But which specific value should the
Supplier choose? Obviously, a realistic assumption is that the Supplier would choose the
value of W1 so as to maximize his own profit as given in Equation (3.15). This gives:
W1* :
D Ec
.
2E
(3.17)
By substituting W1* in Equations (3.14)-(3.16), we obtain B1 W1*
T1 W1*
( W1
–
; S1 W1*
4
–
and
2
3
– . Note that the solitaire scenario with optimal decisions of both players
4
W1* and P1
P1* ) does not lead to the optimal SC profit (as determined under the
centralized scenario).
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To explore the profit functions (3.14)-(3.16) somewhat further, assume that the Supplier
c , i.e., the Supplier decides to sell the products to the Buyer
had chosen the value of W1
c in Equations (3.14)-(3.16) gives B1 (c)
at cost. Substituting W1
and T1 (c)
– , S1 (c)
0
– . Note that when compared to the previous situation the SC profit is larger
( – instead of
3
– ). In fact it is easy to see that W1
4
c maximises the SC profit
function given in (3.16). It is obvious that this situation is very profitable for the Buyer
but not for the Supplier. In other words, there is absolutely no incentive for the Supplier
to optimise the SC profit. Now assume that W1
D
E
. Substituting this value in the profit
functions (3.14)-(3.16) shows that in this case all profits are zero. This demonstrates that
if the price set by the Supplier is too high, the result is that the demand and the SC profit
will be zero.
The results of the solitaire scenario are summarised in Figure 3.2.
P14 Profit
Profit
4ʌ
π
T
T
T
3ʌ
3π/4
1
4
B
B
2ʌ
π/2
ʌ
π/4
0
0
S
S
c
c
W2
W1*
D E W
α β W
Figure 3.2: Profits for Supplier ( S ), Buyer ( B ) and supply chain ( T ) for
various prices W1 under the Solitaire-scenario.
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Example
Throughout this chapter we will use the following example. Let D( P) 100 2 P ,
100 and E
i.e., D
2 . Furthermore, let c = 30.
The results for the numerical example are summarized in the Table 3.1.Ŷ
Scenario
W
P
Q
B
S
T
0
Centralized
n/a
40
20
n/a
n/a
200
1
Solitaire
40
45
10
50
100
150
Table 3.1: Centralized vs. solitaire scenario (Numerical example)
3.5
The Partnership Scenario 2
In the partnership scenario (denoted by subscript 2) we assume that the Supplier and
Buyer jointly determine P2 first and only after that fix W2 .
The following theorem summarizes the results of the partnership scenario.
Theorem 3.1 [Van der Veen & Venugopal, (2001)]
(i)
By forming a full partnership the optimal supply chain profit is achieved.
(ii)
For any wholesale price W1 under the solitaire scenario there is a W2 under the
partnership scenario such that both the Buyer and the Supplier have a higher
profit in partnership scenario compared to the solitaire scenario.
Proof
(i) Since under this scenario it is assumed that the Buyer and the Supplier are working
together in a full partnership, they are interested in optimizing the SC profit, i.e., they
would choose a value for P2 such that the SC profit
T2 ( P2 )
P2 c D EP2 (3.18)
2
The analysis, of the partnership scenario in the subsequent chapters can be performed on similar lines.
Hence, it will not be repeated hereafter.
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is maximized. Clearly, this is exactly the same situation as under the centralized scenario,
so that the optimal price and order quantity are given by P2*
in a SC profit T2 P2*
P0* and Q2*
Q0* , resulting
– . This shows that the optimal SC profit is achieved.
(ii) Under (i) it is shown that the SC profit is maximized. But what about the profits for
the Supplier and the Buyer under the partnership-scenario? Are they also better (greater
or equal) when compared to the profits under the solitaire-scenario? Unlike the SC profit,
the profits for the Buyer and the Supplier do depend on the price W2 . The exact
relationship can be derived from Equations (3.4) and (3.5) by substituting Equations (3.7)
and (3.8). This gives:
B 2 W2
12 D Ec W2 D Ec D Ec (3.19)
4E
for the Buyer and
D Ec W
S 2 W2
1
2
2
12 D Ec c
(3.20)
and S W are linear functions of W
for the Supplier. Clearly, both B2 W2
2
2
2
. It is now
assumed that when forming the partnership the two companies decide that a “fair” price
is a price W2 at which both the Buyer and the Supplier are better off (i.e., have higher
profit) than in the solitaire-scenario. Let, as before, W1* denote the price charged by the
Supplier in the solitaire-scenario. Any price W2 is acceptable to the Buyer as long
as B2 (W2 ) ! B1 (W1 ) . Using Equations (3.14) and (3.19) this is equivalent to:
W2 E (c) 2 2DW1 E (W1 ) 2
: (W2 ) .
2D E c (3.21)
Similarly, any price W2 is acceptable to the Supplier as long as S 2 (W2 ) ! S1 (W1 ) . By
using Equations (3.15) and (3.20) this is equivalent to:
W2 !
E (c) 2 D Ec W1 E (W1 ) 2
: (W2 ) .
D Ec (3.22)
Note that
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COORDINATING PRICING AND REPLENISHMENT DECISION IN A PRICE SENSTITIVE DETERMINISTIC SC
E W1 c !0
2D Ec 2
(W2 ) (W2 )
(3.23)
It follows that (W2 ) ! (W2 ) and, moreover, that (W2 ) (W2 ) if and only if W1
c
in which case there is no win-win. This implies that there is always a price W2 such that
both the Supplier and the Buyer have strictly higher profit in the partnership-scenario
than in the solitaire-scenario (except for the unlikely case that W1
c ). In other words,
win-win situations do actually exist. This completes the proof.Ŷ
The profits under the partnership scenario of the Buyer, Supplier and the SC as functions
of W2 are depicted in Figure 3.3.
Profit
W2
4ʌ
Profit
T
T
ʌ
B
3ʌ
B
3ʌ/4
2ʌ
ʌ/2
ʌ
ʌ/4
S
S
0
0
c
c
W
E
W
W2 = W
W
W2 W
W
P
WW2 = pP22 W 2
W
Figure 3.3: Profits for Supplier ( S ), Buyer ( B ) and SC ( T ) for various wholesale prices
W2 under the Partnership-scenario.
It is to be noted that, unlike in the solitaire scenario, here the maximum SC profit is
always achieved. More specifically, when compared to the SC profit under the solitairescenario, under the partnership-scenario the SC profit value is larger (or equal in case of
W1
c ). The difference in SC profit between the two scenarios is given by:
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CHAPTER
T2 T1 (W1 )
E
W
4
1
c
2
3
(3.24)
where W1 is the price set by the Supplier under the solitaire-scenario. One might wonder
how this additional profit is achieved. This question can be answered by noting that P2* d
P1* and Q2* t Q1* for all realistic values of W2 , i.e., if the SC is optimized then the price is
lower and the quantity ordered is higher. It may be concluded that also the consumers
profit from the collaboration between the Buyer and the Supplier in the sense that the
price of the product is lower. The lower price to the end-consumers leads to a higher
demand and therefore a higher profit of the entire SC.
Example (continued)
For the numerical example W2 is 40 and W2 is 35. Assuming W2 = 37; the results for
the numerical example are summarized in Table 3.2.
Scenario
W
P
Q
B
S
T
-
40
20
-
-
200
0
Centralized
1
Solitaire
40
45
10
50
100
150
2
Partnership
37
40
20
60
140
200
Table 3.2: Results for the partnership scenario (Numerical example)
Note that the partnership scenario leads to the same profit as the centralized scenario (the
SC is coordinated) and that both the Buyer and the Supplier have a higher profit under the
partnership scenario when compared to the solitaire scenario (win-win).Ŷ
The above analysis helps us to conclude that a partnership will always coordinate the SC
and provide win-win opportunities. However, in reality partnerships are very difficult to
create and sustain and pose several implementation issues. In the next section we discuss
the applicability of contract mechanisms, as these mechanisms might be powerful enough
to create SC optimization and win-win opportunities, and implementation is not too
difficult.
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3.6
75
Contract Mechanisms
A supply chain contract is an agreement among different players with respect to different
trade parameters such as pricing, order quantity commitment, periodicity of ordering,
delivery commitment, and quality. For example, the agreement with respect to the pricing
parameter usually concerns:
How much is paid for each unit; and
What additional incentives are involved and how they are paid. This includes
agreement on incentives such as quantity discount, profit sharing, revenue sharing,
credit for returned goods, et cetera.
The format of supply chain contracts varies across industries. Some of the commonly
observed supply chain contracts are quantity discount contract, profit sharing contract,
revenue sharing contract and buy-back contract.
In section 3.7 -3.10 various supply contracts and their ability to coordinate and achieve
win-win opportunities will be reviewed. In the Section 3.7 we start with the revenue
sharing contract.
3.7
Revenue sharing mechanism
Under the revenue sharing mechanism (denoted by subscript 3) the transactions between
the Supplier and Buyer are governed by the Supplier charging a share of the Buyer’s
revenues in addition to the wholesale price. The revenue sharing contract can be
identified by two parameters, namely, a wholesale price W3 and a percentage of the
Buyer’s profit J 3 (0< J 3 <1), that goes to the Supplier. One recent example of revenue
sharing is from video-cassette rental industry (see e.g., Cachon & Lariviere (2005) and
Dana & Spier (2001)). Under the revenue sharing mechanism, the profit functions are:
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CHAPTER
B3 (W3 , Q3 , J 3 )
ª (D Q3 ) º
(1 J 3 ) «
»Q3 W3 Q3
¬ E
¼
3
(3.25)
for the Buyer;
ª (D Q3 ) º
S 3 (W3 , Q3 , J 3 ) W3 Q3 J 3 «
»Q3 cQ3
¬ E
¼
(3.26)
for the Supplier; and
T3 (Q3 )
ª (D Q3 ) º
«
»Q3 cQ3
¬ E
¼
(3.27)
for the SC.
The following theorem gives the main results on the revenue sharing mechanism.
Theorem 3.2
(i)
The revenue sharing contract [W3 ; J 3 ] with W3*
(1 J 3 )c will lead to a
coordinated Supply Chain.
(ii)
For any price W1 under the solitaire scenario, there is a value for J 3 and
W3* under the revenue sharing scenario [W3* ; J 3 ] such that both the Supplier and
the Buyer achieve a higher profit than the realized profits under the solitaire
scenario.
Proof
(i) The order size which will optimize the SC profit can be obtained from Equation (3.8)
as:
(D Ec)
Q0*
.
(3.28)
2
The optimal order size for the Buyer can be obtained from Equation (3.25) as:
Q3*
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D (1 J 3 ) EW3
.
2(1 J 3 )
(3.29)
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77
To achieve that the Buyer order the SC optimal quantity while still acting in his own best
interest, the value of W3 should be such that the right-hand side of Equations (3.28) and
Equation (3.29) are the same. This occurs when:
W3*
(1 J 3 )c .
(3.30)
Note that this implies that the Supplier sets his wholesale price at a level lower than his
cost of manufacturing. However, this might still be acceptable to the Supplier as he is
also receiving a share of the Buyer’s revenues. The profits for the players at this value of
W3* can be obtained as follows:
B3 (J 3 )
ª (D Ec) 2 º
«
» (1 J 3 ) = (1 J 3 ) –
¬ 4E
¼
(3.31)
ª (D E c) 2 º
«
»J 3 = J 3 –
¬ 4E
¼
(3.32)
for the Buyer;
S3 (J 3 )
for the Supplier; and
T3 (J 3 )
(D Ec) 2
4E
3
(3.33)
for the SC. It follows immediately from Equation (3.33) that if (3.30) is satisfied, the SC
is coordinated.
(ii) It is clear from the Equations (3.31)-(3.32) that the profits for the Supplier and the
Buyer are dependent on J 3 , hence J 3 can be used to divide the profits between them in
the required proportions. A win-win situation can be achieved if the profit with revenue
sharing is higher than the profit in a solitaire scenario. The profit for the Supplier with
revenue sharing is greater than his profit in a solitaire scenario iff S3 (J 3 ) ! S1 (W1 ) . This
is equivalent to:
J3 !
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S1 (W1 )
: (J 3 ) .
3
(3.34)
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CHAPTER
3
Also, the profit for the Buyer with revenue sharing should be greater than his profit in a
solitaire scenario, i.e., B3 (J 3 ) ! B1 (W1* ) . This happens iff:
J3 3 B1 (W1 )
: (J 3 ) .
–
(3.35)
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. From Equation (3.34) and Equation (3.35) we obtain:
(J 3 ) (J 3 ) 3 T1 (W1* )
! 0.
3
(3.36)
Clearly, expression (3.36) will always be greater than zero as the SC profits with
centralization will be greater than those in the solitaire scenario (assuming W1 > c). When
the profits under a centralized scenario are equal to the profits under the solitaire scenario
the above equation will be equal to zero. In that case the upper and the lower bound of the
revenue sharing mechanisms will be equal in which case there are no win-win
opportunities. This concludes the proof.Ŷ
3.7.1
Methods to divide the overall improved profit
In reality, a key issue in all the coordination and contract mechanisms is choosing the
specific value of contract parameters so that the enlarged profit is divided between the
Supplier and the Buyer in a reasonable way. The main factors that drive this decision are:
(1) Proportion of investments (cost) incurred by players in delivering the product and
service to customers;
(2) The power of the players in the supply chain.
Below two possible methods to divide the overall improved profit are provided. Both
methods will be demonstrated in the setting of the revenue sharing mechanism but can
also be applied to the other mechanisms.
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COORDINATING PRICING AND REPLENISHMENT DECISION IN A PRICE SENSTITIVE DETERMINISTIC SC
In the so-called equal profit sharing method the goal is to share the enlarged profit
equally. This rule would make sense when the Supplier and the Buyer has equal power in
the SC or when both the players have an equal share of investment in the process of
delivering the product to the end-consumer. The equal profit sharing method is applied if
the parameter J 3 is set as follows:
J 3Eq :
(J 3 ) (J 3 ) .
2
Under the revenue sharing contract [W3*
as:
33
B3 (J 3Eq )
8
for the Buyer; and
S3 (J 3Eq )
53
8
(1 J 3 )c; J 3
(3.37)
J 3Eq ] , the profits can be obtained
3 3
4 8
(3.38)
3 3
2 8
(3.39)
for the Supplier. Note that indeed both profits increase with the same amount. As per the
McKinsey (1991) survey, strategic alliances with equal profit sharing rule are the most
successful alliances; see Amaldoss et al. (2000). The advantage of this rule is that there is
no need to monitor the players’ investments.
Another realistic possibility would be that the Supplier and Buyer agree that when
working together, the percentage of growth in profit compared to the base case scenario
should be equal for both companies. So, this so-called proportional profit sharing method
takes the individual investments (costs) and power of the two companies into account.
The proportional profit Sharing method is applied if the parameter J 3 is set as follows:
§
·¸(J
¸¹
B1 W1*
*
*
© S1 W1 B1 W1
J 3Pr : ¨¨
3
Under the revenue sharing contract [W3*
as:
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·¸(J
¸¹
§
S1 W1*
) ¨¨
*
*
© S1 W1 B1 W1
(1 J 3 )c; J 3
3
) .
(3.40)
J 3Pr ] , the profits can be obtained
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CHAPTER
B3 (J 3Pr )
43
12
4
3
S3 (J 3Pr )
83
12
4
3
3
3
( )
4
(3.41)
§3·
¨ ¸
©2¹
(3.42)
for the Buyer; and
for the Supplier.
Example (continued)
The results for the numerical example are summarized in the Table 3.3.
Scenario
W
Q
B
S
T
0
Centralized
n/a
20
n/a
n/a
200
1
Solitaire
40
10
50
100
150
Revenue sharing
15
20
75
125
200
10
20
66.7
133.3
200
2
Equal sharing: J = 0.625
Revenue sharing
Proportional sharing J = 0.67
Table 3.3: Revenue sharing results (Numerical example)
From Table 3.3 it can be observed that the revenue sharing mechanism results in the same
SC profit as the centralized scenario, i.e., the SC is coordinated. Also win-win occurs
when compared to the solitaire scenario. At equal sharing both parties add 25 to their
profits; at the proportional sharing both add 33% when compared to the solitaire
scenario.Ŷ
In the next section, we analyze the profit sharing mechanisms.
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3.8
81
Profit Sharing Mechanism
In the profit sharing mechanism (denoted by subscript 4), the transactions between the
Supplier and Buyer are governed by the Supplier charging the Buyer a share of his profits
plus a wholesale price per unit sold. More specifically, the profit sharing mechanism can
be identified by two parameters, namely, the wholesale price W4 and a percentage of the
Buyer’s profit G 4 (0< G 4 <1) that goes to the Supplier. The first paper investigating the
profit sharing mechanism to achieve channel coordination was Jeuland & Shugan (1983).
Under the profit sharing contract [W4 ; G 4 ] , the profit functions are:
§ ª D Q4 º
(1 G 4 )¨¨ «
» W4
©¬ E ¼
B4 (W4 , Q4 , G 4 )
·
¸Q4
¸
¹
(3.43)
for the Buyer;
S 4 (W4 , Q4 , G 4 )
W
4
§ ª (D Q4 ) º
·
c Q4 G 4 ¨¨ «
» W4 ¸¸Q4
¼
©¬ E
¹
(3.44)
for the Supplier; and
T4 (Q4 )
B4 S 4
§ ª (D Q4 ) º
·
¨«
» c ¸¸Q4
¨
¼
©¬ E
¹
(3.45)
for the SC.
The following theorem highlights the usefulness of the profit sharing mechanism.
Theorem 3.3
(i)
The Profit sharing contract [W4* ; G 4 ] where W4*
c will lead to a coordinated
Supply Chain.
(ii)
For any price W1 under the solitaire scenario, there is a value for G 4 and
W4* under the profit sharing contract [W4* ; G 4 ] such that both the Supplier and the
Buyer achieve higher profits than the realized profits under the solitaire scenario.
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CHAPTER
3
Proof
(i) The order size which will optimize the SC profit can be obtained from Equation (3.8)
as:
Q0* 12 (D Ec)
(3.46)
The optimal order size for the Buyer can be obtained from Equation (3.43) as:
Q4*
1
2
(D EW4 ) .
(3.47)
It follows that the optimal order size coincides with the SC optimal order size iff W4*
c.
In other words, the optimal quantity will indeed be ordered by the Buyer when the
Supplier’s wholesale price is equal to his cost of manufacturing. This might still be
acceptable to the Supplier as he is also receiving a share of the Buyer’s profit. Assuming
W4
c , the profits for the players can be obtained as follows:
B4 (G 4 )
ª (D Ec) 2 º
«
» (1 G 4 )
¬ 4E
¼
(3.48)
ª (D E c) 2 º
«
»G 4
¬ 4E
¼
(3.49)
for the Buyer;
S 4 (G 4 )
for the Supplier; and
T4
(D Ec) 2
4E
3
(3.50)
for the SC. It follows directly from Equation (3.50) that the profit sharing mechanism will
optimize the SC.
(ii) A win-win is said to be achieved if the profits of the two players with profit sharing is
higher than the profits in a solitaire scenario. First, the profit for the Supplier under the
profit sharing contract should be greater than his profit in a solitaire scenario. Clearly,
S 4 (G 4 ) ! S1 (W1 ) iff:
G4 !
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S1 (W1 )
: (G 4 ) .
3
(3.51)
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COORDINATING PRICING AND REPLENISHMENT DECISION IN A PRICE SENSTITIVE DETERMINISTIC SC
Second, the profit for the Buyer with profit sharing should be greater than his profit in a
solitaire scenario. Note that B4 (G 4 ) ! B1 (W1 ) iff:
G4 3 B1 (W1 )
: (G 4 ) .
3
(3.52)
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. It can be observed that:
(G 4 ) (G 4 ) 3 T1 (W1 )
! 0.
3
(3.53)
Clearly, expression (3.53) will always be greater than zero as the SC profits with
centralization will be greater than those in the solitaire scenario (assuming W1* ! c ).
When the profits under a centralized scenario are equal to the profits under the solitaire
scenario the above equation will be equal to zero. In that case the upper and the lower
bound on the profits sharing mechanisms will be equal in which case there are no winwin opportunities. This concludes the proof.Ŷ
Example (continued)
Assuming G5 = 0.625, the results for the various scenarios can be found in the Table 3.4.
Scenario
W
Q
G
B
S
T
0
Centralized
n/a
20
n/a
n/a
n/a
200
1
Solitaire
40
10
n/a
50
100
150
4
Profit sharing mechanism
30
20
0.625
75
125
200
Table 3.4: Profit sharing results (Numerical example)
From the Table 3.4 it can be seen that under the Profit sharing mechanism [W=30;G4=
0.625] the SC is coordinated (T4 = T0) Also, when compared to the solitaire scenario,
win-win is achieved. In fact, this happens iff 0.5 < G4 < 0.75.Ŷ
In the next sub section we discuss the quantity discount and the license fee mechanisms.
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3.9
CHAPTER
3
Quantity discount & license fee mechanism
With the quantity discount mechanism (denoted by subscript 5), the Supplier fixes a base
price O5 and charges an additional price P 5 which is a decreasing function in Q5 . At its
simplest form the price at which the Supplier sells the product to the Buyer is dependent
upon the order quantity. This is given by:
W5 (Q5 ) O5 P5
Q5
.
(3.54)
The price function in Equation (3.54), yields the following profits:
S 5 (O5 , P 5 , Q5 ) (O5 c)Q5 P 5
(3.55)
§ ª D Q5 º
·
B5 (O5 , P 5 , Q5 ) ¨¨ «
O5 ¸¸Q5 P 5
»
©¬ E ¼
¹
(3.56)
for the Supplier;
for the Buyer; and
(3.57)
§ ªD Q5 º ·
T5 (Q5 ) ¨¨ «
» c ¸¸Q5
©¬ E ¼ ¹
for the SC.
The following theorem describes the channel coordination possibilities of the quantity
discount mechanism.
Theorem 3.4
(i)
The quantity discount contract [O*5 ; P 5 ] with O*5
c leads to a coordinated Supply
Chain.
(ii)
For any price W1 under the solitaire scenario, there are values of P 5 under the
quantity discount contract [O*5 ; P 5 ] , such that both the Supplier and the Buyer
achieve higher profits than the realized profits under the solitaire scenario.
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85
Proof
(i) The order quantity which will optimize the SC profit can be obtained from Equation
(3.8) as:
Q0*
1
2
(D Ec) .
(3.58)
The optimal order quantity for the Buyer can be obtained from Equation (3.56) as:
Q5*
1
2
(D EO5 ) .
(3.59)
It follows that in order to ensure that the Buyer has the incentive to choose the SC
optimal order the value of O5 should be set such that O*5
c.
Substituting this value of O5 in (3.55)-(3.57) yields the following profits:
T5
(D Ec) 2
4E
3
(3.60)
for the SC,
S5 (P5 )
P5
(3.61)
for the Supplier, and
B5 ( P 5 ) 3 P 5
(3.62)
for the Buyer. It follows immediately from Equation (3.60) that for the chosen value
of O5 , the SC is optimized.
(ii) A win-win situation is said to be achieved if the profit with the quantity discount
contract is higher than the profit in a solitaire scenario. First, the profit for the Supplier
with quantity discount should be greater than his profit in a solitaire scenario,
i.e., S5 ( P5 ) ! S1 (W1 ) , which is equivalent to:
P5 !
(D E c) 2
: ( P5 ) .
8E
(3.63)
Second, the profit for the Buyer with quantity discount should be greater than his profit in
a solitaire scenario. i.e., B5 ( P5 ) ! B1 (W1 ) , which is equivalent to:
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CHAPTER
P5 3(D E c) 2
: ( P5 ) .
16 E
3
(3.64)
It remains to be proved that the difference between the upper and the lower bound
obtained in the above Equations (3.63) and (3.64) will always be positive. This is easily
shown by observing that:
( P5 ) ( P5 ) (D Ec) 2
! 0.
16 E
(3.65)
This completes the proof.Ŷ
Example (continued)
The results for the numerical example are summarized is the Table 3.5.
Scenario
W
Q
O
P
B
S
T
0
Centralized
n/a
20
n/a
n/a
n/a
n/a
200
1
Solitaire
40
10
n/a
n/a
50
100
150
5
Quantity discount
n/a
20
30
125
75
125
200
Table 3.5: Quantity discount results (Numerical example)
Assuming P5 = 125, it can be seen that when compared to the solitaire scenario, win-win
is achieved. In fact, this happens iff 100 < P5 < 150. Furthermore, it can be seen that
under the Profit sharing contract [O*5
30; P 5
125] , the SC is coordinated (T5 = T0).Ŷ
With the license fee contract (denoted by subscript 6), the Supplier gets a fixed
amount L6 in addition to the price W6 per item. The license fee mechanism is also called
the two-part tariff mechanism. Moorthy (1987) analyzed the license fee mechanism in the
same setting as Jeuland & Shugan (1983). In the latter paper a coordinating quantity
discount contract was designed, whereas Moorthy (1987) designed the license fee
mechanism.
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87
It is easy to see that a License fee contract with L6 and W6* has exactly the same effect as
a quantity discount contract with P 5 and O5 if P 5
L6 and O*5
W6* .
3.10 Conclusions
Table 3.6 provides an overview of the various contract mechanisms discussed in this
chapter.
Equivalent
mechanisms
Profit sharing,
Revenue
sharing
Quantity
discount,
License fee
Profit sharing,
quantity
discounts
Conditions for
equivalence
relationship to hold
For profit sharing :
W=c
For revenue sharing:
W = (1-J)c
Perfect equivalence
between the parameters
of the two mechanisms.
The conditions for
coordination are the
same for both of these
mechanisms. The
bounds on a win-win
situation are the same
for both of these
mechanisms.
P G T
P G T
(SC profit in the
centralized scenario
relates the contract
parameters)
Mechanism preference
Properties of contract
mechanisms
From an implementation
perspective, revenue
sharing is much simpler
since the revenue is an
easier metric to evaluate,
and the profit figures of
different organizations
and businesses are often
disputed.
These mechanisms share both
risk and rewards as the
parameters of the contract
mechanism are based on
actual sales.
From an implementation
perspective the license fee
mechanism is much
simpler (Moorthy 1987).
Both these mechanisms are
based on reward sharing only.
x With the quantity
discount contract the
parameters are based on
purchases rather than
sales.
x The Buyer has to pay the
license fee which is
independent of the
quantity he sells.
x
From an implementation
perspective the quantity
discount contract is
simpler since there is no
necessity to track Buyer’s
profits.
x
The profit sharing
mechanism shares both
the risks and rewards
between the players.
With the quantity
discount contract the
parameters are based on
purchases rather than
sales, it does not share the
risk.
Table 3.6: Summary of the insights from the contract analysis
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3
Our analysis with the contract mechanisms has led to the following insights:
1) Both revenue sharing and profit sharing can coordinate the SC. Interestingly, both the
mechanisms provide win-win situations for the same range of parameter values and
will yield the same profits for a considered revenue or profit sharing percentage.
However, from an implementation point of view, the revenue sharing mechanism will
be simpler since the profit figures of different companies and businesses are often
disputed. Both these mechanisms have the ability to share “risks” and “rewards” as
the parameters of these contract mechanisms are based on actual sales.
2) Similarly, the quantity discount and the license fee mechanisms have the ability to
coordinate the SC, and they can provide win-win opportunities for the same range of
parameter values. An equivalence relationship between the parameters of the quantity
discount and the license fee mechanism is obtained. These mechanisms do not share
the risk as the parameters are based on the Buyer’s purchases rather than sales.
3) The parameters of the quantity discount and the profit sharing mechanism are related
with the SC profit in the centralized scenario. However, from an implementation
perspective, the quantity discount contract is simpler since there is no necessity for
the Supplier to track the Buyer’s profits. The quantity discount contracts do not share
the risk as the parameters are based on the Buyer’s purchases rather than sales where
as the profit sharing mechanism shares both the risks and the rewards.
A possible extension to this study is to design the contract mechanisms when there is
asymmetry of information between the Buyer and the Supplier (i.e., the Buyer has more
information about the end-consumer demand than the Supplier). It would be interesting to
see if different mechanisms can coordinate the SC and provide win-win opportunities.
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89
Chapter 4
Coordinating Pricing and Replenishment Decisions in a Supply Chain
with Increasing Marginal Cost 3
Chapter Synopsis
In this chapter, we consider the replenishment decisions in a Supply Chain (SC) in which
both the Buyer and the Supplier incur increasing marginal costs which are represented by
quadratic functions of their ordered/produced quantities. Assuming a deterministic endconsumer demand, it is shown that a decentralized SC results in sub-optimal solutions.
The above setting was studied earlier in a classic paper in accountancy literature, namely
Hirshleifler (1956), and later in Ronen & McKinney (1970). These two papers designed
transfer pricing mechanisms to coordinate the replenishment decisions among different
divisions of the same firm. We show that Hirshleifler’s method of transfer pricing does
not provide win-win opportunities. Furthermore, Ronen & McKinney’s method
coordinates and provides win-win. However, it requires accounting adjustments at the
corporate level. Clearly, for the SC where the entities are independent organizational
units, win-win opportunities are necessary and corporate level accounting adjustments are
not possible. To overcome such difficulty, in this chapter, four contract mechanisms for
the above setting are designed, namely the revenue sharing, profit sharing, quantity
discount and the license fee mechanisms. It is shown that revenue sharing coordinates the
SC but does not provide win-win opportunities. However, the profit sharing, quantity
discounts and license fee mechanisms are shown to coordinate the SC and provide winwin opportunities. In this sense the mechanisms are superior to the results in Hirshleifler
(1956) and Ronen & McKinney (1970).
3
This Chapter is a revised, updated and elaborated version of the paper presented at the 11th annual
EurOMA doctoral conference at INSEAD France in June 2004 [Reference: Nalla, V. R, J.A.A van der
Veen, and V. Venugopal (2004)].
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4.1
CHAPTER
4
Introduction
This chapter designs and demonstrates the applicability of incentive or contract
mechanisms in a SC which consists of a Supplier and a Buyer catering to an endconsumer demand. The Supplier firm offers a quantity of products to the Buyer firm at a
specified price. It is assumed that both the Buyer and Supplier incur increasing marginal
costs, which are expressed as a quadratic cost function. For a practical example of such a
setting, consider the case of a manufacturer of heavy equipment such as electric turbines,
jet engines and ship building. This would require packets of capacity for manufacturing
every single unit during a given period of time. For producing additional units, the
manufacturer needs to establish new facilities, hire new personal, and procure new
logistic capabilities. This causes costs to increase proportionally more than the increase in
production, hence the marginal costs are increasing. Besides its practical applicability, the
model in this chapter was inspired by a seminal paper from the accountancy literature,
namely Hirshleifler (1956).
Hirshleifler (1956) and later Ronen & McKinney (1970) have designed transfer pricing
mechanisms to coordinate replenishment decisions among the different divisions of the
same firm. Both of these studies have considered a similar setting as discussed in this
chapter. We will review the Hirshleifler (1956) and Ronen & Mckinney (1970) methods
of transfer pricing and outline their drawbacks. To overcome these drawback, four
different contract mechanisms, the revenue sharing, profit sharing, quantity discount and
license fee mechanisms, are designed and analyzed.
The remaining part of this chapter is organized as follows. In the next section we
introduce the basic model and analyze the performance of the centralized scenario.
Subsequently, we test the performance under the decentralized scenario. Then the
Hirshleifler (1956) and Ronen & McKinney (1970) transfer mechanisms are discussed,
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
after which we design various contract mechanisms. Finally, the study is concluded and
some managerial insights are provided.
4.2
Model and Basic analysis
Supplier
C
O
N
S
U
M
E
R
S
Buyer
Price: P
c S (Q) D S Q E S Q 2
cB (Q)
D BQ E BQ 2
p
Figure 4.1: SC model
Consider a two-echelon SC with a Buyer and a Supplier, see Figure 4.1. The Supplier
offers a quantity of products to the Buyer at a price W per unit. It is assumed that the
product has a short life cycle and the Buyer places the order only once, i.e., reordering is
not possible and there is no stock from previous periods. The Supplier incurs a
deterministic manufacturing, transportation and facility cost of (D S Q E S Q ) , where
2
D S and E S are constants specific to the Supplier, and Q is the quantity supplied. Being a
monopolist, the Supplier is free to set the price W at which he will sell the product to the
Buyer.
The
Buyer
will
incur
deterministic
additional
processing
costs
of
2
(D B Q E B Q ) , where D B and E B are constants specific to the Buyer’s cost function,
and Q is the quantity purchased. The demand is assumed to be deterministic and the final
selling price of the product p is determined exogenous (set by the market). It is assumed
that the supplied quantity will be equal to ordered quantity. More specifically, the
following sequence of the events takes place in the SC:
x
The final selling price p of the product is exogenously determined. The Buyer or the
Supplier cannot influence the final consumer price;
x
The Supplier, knowing both its own and the Buyer’s cost functions, anticipates the
Buyer’s response and chooses the wholesale price W that will maximize his profit;.
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x
CHAPTER
4
Based on the wholesale price W fixed by the Supplier, the Buyer will order the
quantity Q which will optimize his profit;
x
Finally, the Buyer sells the product to the end-consumer market.
The Supplier can set W such that his profit, given by:
WQ (D S Q E S Q 2 ) .
S (W )
(4.1)
is maximized. The Buyer charges a price p to the end-consumer and will determine his
order quantity Q such that the profit, given by:
B (Q)
( p W )Q (D B Q E B Q 2 )
(4.2)
is maximized. The total SC profit is determined by:
T
SB
pQ (D S D B )Q ( E S E B )Q 2
(4.3)
Note that the expression for total SC profit T does not depend on the wholesale price W,
but only on the order quantity Q. In other words, W can be considered as an internal price
if the entire SC is considered.
We start our analysis with the so-called centralized scenario (which will be represented
by subscript 0). At the centralized scenario, the SC is considered as a single entity, i.e.,
the objective is to find the order size that maximizes SC profit. From Equation (4.3), the
SC optimal order quantity can be obtained as:
Q0*
( p DS DB )
.
2( E B E S )
(4.4)
The SC profit with the optimal order quantity from Equation (4.4) can be obtained as:
T0
( p D S D B )2
:– .
4( E B E S )
(4.5)
Example
Throughout this chapter, we will use the following numerical example. Let the cost
function for the Supplier be: c S (Q)
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20Q 2Q 2 , i.e., D S
20, and E S
2 . Furthermore,
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
let the cost function for the Buyer be: c B (Q) 30Q Q 2 , i.e., D B
assume that the selling price of the final product P
30 and E B
93
1 and
110 .
It follows that the optimal order quantity is Q0= 10. The associated optimal SC profit is
given by T0 = 300.Ŷ
In the next section, we analyze the solitaire scenario.
4.3
Solitaire scenario analysis
In the so-called solitaire scenario (also known as the decentralized scenario) it is
assumed that both the Supplier and the Buyer act in their own best interest without
considering each other. In this scenario, the Supplier sets its wholesale price, and then the
Buyer determines a quantity that maximizes its profit.
Assume the Supplier has set a price W1 (the decision variables in the solitaire scenario are
represented by subscript 1). Obviously, the Buyer wants to maximize his profit and will
choose Q1 such that his profit is maximized. Using Equation (4.2), the optimal order
quantity for the Buyer can be obtained as:
Q1*
1
2E B
( p W1 D B ) .
(4.6)
If the Buyer orders a quantity that is optimal for his business, it would result in the
following profits:
B1 (W1 )
p W1 D B 2
(4.7)
4E B
for the Buyer;
§ p W1 D B
S1 (W1 ) ¨¨
2
© 4( E B )
·
¸¸ (2E B E S )W1 2D S E B D B E S E S p
¹
(4.8)
for the Supplier, and
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CHAPTER
§ p W1 D B
T1 (W1 ) ¨¨
2
© 4( E B )
·
¸¸ ( E S E B )W1 D B E S D B E B 2 E BD S ( E B E S ) p
¹
4
(4.9)
for the SC.
Note that the Buyer’s order quantity and all profits (4.6)-(4.9) do depend on the
wholesale price W1 . This implies that W1 is not only used for dividing the overall profit
among the players, but also influences the size of the overall SC profit. Obviously, the
Supplier would like to choose W1 such that his profit S1 (W1 ) is maximized. It can be
determined from Equation (4.8) that S1 (W1 ) is maximized at:
p (E B E S ) D B (E B E S ) D S E B
(2E B E S )
W1*
(4.10)
Using W1* as the wholesale price results in the following profits:
B1
E B ( p D B D S )2
4(2 E B E S ) 2
(4.11)
( p D S D B )2
4(2E B E S )
(4.12)
( p D B D S ) 2 (3E B E S )
4(2E B E S ) 2
(4.13)
B1 (W1* )
for the Buyer;
S1
S1 (W1* )
for the Supplier; and
T1
T1 (W1* )
for the SC. In comparing Equations (4.5) and (4.13), we obtain:
T0 T1
§ (E B ) 2
·
¨¨
¸ 3 ! 0.
2 ¸
© (2 E B E S ) ¹
(4.14)
It follows that the solitaire scenario leads to sub-optimal solutions.
For comparison reasons, we now investigate which wholesale price achieves the optimal
SC profit in this setting (this scenario will be described by subscript 2). In order to
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
95
achieve the optimal profit for the SC, the wholesale price W2 must be set to the value that
maximizes Equation (4.9). The wholesale price W2 which gives the optimal SC profit can
be obtained as:
W2*
ES p DS EB DBES
.
(E S E B )
(4.15)
For the wholesale price of W2* obtained in Equation (4.15), the profits for the SC and the
players can be obtained as follows:
T2
T2 (W2* )
( p D S D B )2
4( E B E S )
–
(4.16)
for the SC;
B2
§ EB
B2 (W2* ) ¨¨
© EB ES
·§ ( p D S D B ) 2 · § E B
¸¸¨¨
¸¸ = ¨¨
¹© 4( E B E S ) ¹ © E B E S
·
¸¸ –
¹
(4.17)
·§ ( p D S D B ) 2 · § E S
¸¸¨¨
¸¸ = ¨¨
¹© 4( E B E S ) ¹ © E B E S
·
¸¸ –
¹
(4.18)
for the Buyer; and
S2
§ ES
S 2 (W2* ) ¨¨
© EB ES
for the Supplier.
As was to be expected, the SC is coordinated under Scenario 2. To see whether win-win
is achieved compared to the solitaire scenario we derive the following.
The difference between the Buyer’s profit at Scenario 2 and the profit that Buyer realizes
under the solitaire scenario is:
B2 B1
1
E B ( p D S D B )2
4
§¨¨ (E
©
·
3( E B ) 2 2 E B E S
¸.
2
2 ¸
B E S ) (2 E B E S ) ¹
(4.19)
The value in Equation (4.19) will always be positive. The difference between the
Supplier’s profit at Scenario 2 and the profit that Supplier realized under the solitaire
scenario is given by:
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CHAPTER
S 2 S1
( p D S D B )2
2
EB .
2
4(2E B E S )( E B E S )
4
(4.20)
It is clear from Equation (4.20) that Supplier has a lower profit under Scenario 2 as
compared to Scenario 1. Clearly, the Supplier will never set the wholesale price at W2 , as
it leads to lower profit when compared to the solitaire scenario.
Example (continued)
Table 4.1 provides the results for the numerical example in all three scenarios discussed
so far.
Scenario
W
Q
B
S
T
-
10
-
-
300
0
Centralized
1
Solitaire
65
7.5
56.25
225
281.25
2
SC optimal W
60
10
100
200
300
Table 4.1: Numerical example results for three different scenarios
It can be seen that that the solitaire scenario does not coordinate the SC whereas Scenario
2 does. Compared to the solitaire scenario, in Scenario 2 the Buyer’s profit is higher and
the Supplier’s profit is lower.Ŷ
Figure 4.2 summarizes the results obtained so far (the data used stem from the numerical
example).
From the analysis of the solitaire scenario we can make the following conclusion:
1) The SC profit is not fixed but depends on the value of W;
2) Local optimization of both Buyer and the Supplier does not lead to global
optimization;
3) The Supplier does not have any incentive to optimize the SC because this would
reduce his own profit.
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
Profitsunder
under Solitaire
Profits
Solitaire
300
300
300
300
281,25
281,25
250
250
225
225
200
Profit
Profits
225
225
200
200
200
150
150
100
100
100
100
56,25
50
50
0
56,25
0
0
50
0
50
55
60
55
65
60
Profit Buyer
Profit Buyer
70
65
W3
Profit Supplier
0
80
75
70
0
75
80
W2
Profit Total Supply Chain
Profit Supplier
Profit Total Supply Chain
Figure 4.2: Profits for the Buyer, Supplier and SC under the solitaire scenario
4.4
Intra-firm transfer pricing mechanisms
Hirshleifler (1956) and Ronen & McKinney (1970) have considered a setting similar to
the model presented in this chapter. However, in these two papers the Buyer and the
Supplier are assumed to be divisions of the same firm. Note that in their setting the
wholesale price is seen as a corporate internal transfer price.
In his approach (denoted by subscript 3 here), Hirshleifler (1956) suggests that the
marginal costs for the Supplier division and the Buyer division should be equal to their
marginal revenue, i.e.,
D S 2 E S Q3 ; and
(4.21)
( p W3 ) D B 2E B Q3
(4.22)
W3
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CHAPTER
4
Solving Equations (4.21) and (4.22) yields the following values for Q3 and W3 :
Q3*
W3*
p (D S D B )
2( E S E B )
Q2* ; and
ES p DS EB DBES
(E S E B )
(4.23)
W2* .
(4.24)
It follows that the profits for the Buyer and the Supplier are the same as their profits when
the Supplier chooses the wholesale price, which is derived under Scenario 2, i.e.,
Scenario 2 and 3 lead to exactly the same results. In our language, the key result in
Hirshleifler (1956) was that his method, unlike the solitaire scenario, leads to a
coordinated chain, i.e., leads to a maximum profit for the firm. However, it can also be
observed that when compared to the solitaire scenario, Hirshleifler’s approach does not
lead to win-win opportunities. However, since the two divisions belong to the same firm,
corporate headquarters can influence the wholesale price and order quantity and ensure
that optimal quantities for the entire firm are chosen without bothering too much about
the profits in the departments. So, in such a setting providing win-win opportunities is
desired but not a necessary condition. However, for a SC where the Buyer and the
Supplier are autonomous companies, providing win-win opportunities is no less than a
necessary condition. This leads to the conclusion that Hirshleifler’s method of fixing
transfer pricing cannot be used for Supply Chains consisting of autonomous
organizations 4.
To overcome the difficulties of providing win-win opportunities, Ronen and McKinney
B
S
(1970) suggested a system of two transfer prices (denoted by [W4 ,W4 ] ), one for the
Buyer and one for the Supplier (where the subscript 4 refers to their suggested scenario).
The price each entity pays is set as equal to the average cost of the other party. In this
approach, the price the Buyer pays the Supplier for a quantity Q4 is given by:
4
In Chapter 1 we distinguish between various levels of SCs. Using this concept it can be seen that
Hirshleifler’s approach works at SC Level 2 but not at SC Level 3.
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B
W4 (Q4 )
c S (Q4 )
Q4
D S E S Q4 ;
99
(4.25)
And the price the Supplier receives from the Buyer for delivering Q4 units is:
§ c (Q ) ·
p ¨¨ B 4 ¸¸
© Q4 ¹
W4S (Q4 )
p (D B E B Q4 ) .
(4.26)
In this approach “corporate headquarters” takes responsibility for the difference in prices
(difference between the price paid by the Buyer and that received by the Supplier). Using
the wholesale prices in Equation (4.25) and (4.26), the profits for the Buyer, Supplier and
the SC can be obtained as:
B4 (Q4 )
(4.27)
( p D S D B )Q4 E B E S Q4 ; and
(4.28)
2
S 4 (Q4 )
T4 (Q4 )
p D S D B Q4 E B E S Q4 2 ;
S 4 B4 W4S W4B Q4
( p D S D B )Q4 ( E B E S )Q4
2
(4.29)
It is clear from the above equations that the Supplier’s profit is exactly the same as that of
the Buyer and also exactly the same as that of the SC. Moreover, the profit function is
also exactly same as the SC profit function in the centralized scenario. Therefore, if the
Supplier and the Buyer optimize their own situations, they will automatically optimize
the SC. Note that here the SC profit is not equal to the sum of the profits of the Buyer and
Supplier. This is due to the fact that corporate headquarters (i.e., the SC) are to
compensate for the difference in price paid by the Buyer and the price received by the
Supplier. But when everything is summed, it can be observed that the SC is optimized
and the company is better off with the two-price system than it was in the solitaire
scenario. In this two-price system, the SC is optimized and a win-win scenario is
achieved. The advantage of the two-price system is that both parties have direct
incentives to optimize the corporate profit simply because this is equal to optimizing their
own situations. Unfortunately, this mechanism requires the involvement of headquarters,
which will not be feasible for the SC in which each company is an independent
autonomous entity. We can conclude that the Ronen and McKinney (1970) method may
work for an intra-firm SC but will not help SCs made up of autonomous firms.
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CHAPTER
4
Example (continued)
The results for the numerical example are summarized in Table 4.2.
Scenario
0
Centralized
1
Solitaire
2;3
Hirshleifler
4
Ronen & McKinney
W4
W
Q
B
S
T
-
10
-
-
300
65
7.5
56.25
225
281.25
60
10
100
200
300
10
300
300
300
B
40 ;
S
70
W4
Table 4.2: Hirshleifler and Ronen & McKinney results (Numerical example)
Note that, unlike the Hischleifer mechanism, Ronen & McKinney’s mechanism provides
win-win. Also note that, the corporate internal subsidy is equal to 30 per unit, with a total
of 300.Ŷ
We design four different contracts, namely the revenue sharing, profit sharing, quantity
discount, and license fee mechanisms to achieve coordination and win-win opportunities.
In the next section we design the revenue sharing mechanism.
4.5
Revenue sharing mechanism
In the revenue sharing mechanism (denoted by subscript 5), the transactions between the
Supplier and Buyer are governed by the Supplier receiving a share of the Buyer’s
revenues. The revenue sharing contract [W5 , J 5 ] can be identified by two parameters,
namely, the wholesale price W5 and a percentage of the Buyer’s revenue J 5 (0 < J 5 < 1)
that goes to the Supplier. The profit functions for the players and the SC using the
revenue sharing contract are:
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S 5 (W5 , Q5 , J 5 ) W5 Q5 J 5 pQ5 (D S Q5 E S (Q5 ) 2 )
101
(4.30)
for the Supplier;
B5 (W5 , Q5 , J 5 )
(1 J 5 ) pQ5 W5 Q5 (D B Q5 E B (Q5 ) 2 )
(4.31)
pQ5 (D S D B )Q5 ( E S E B )(Q5 ) 2
(4.32)
for the Buyer; and
T5 (Q5 )
S 5 B5
for the SC.
The performance of the revenue sharing mechanism is summarized in Theorem 4.1.
Theorem 4.1
The Revenue sharing contract [W5* , J 5 ] with
W5*
(1 J
5
)E S J 5 E B p D S E B D B E S
ES EB
will lead to a coordinated SC for all 0 < J 5 < 1 .
Proof
The order size which will optimize the Buyer’s profit can be obtained from Equation
(4.31) as:
(4.33)
(1 J 5 ) p W5 D B
Q5*
.
2E B
Recall from Equation (4.4) that the order size which will optimize SC profit is given by:
Q0*
p (D S D B )
.
2( E S E B )
(4.34)
In order to achieve that the Buyer will act in his own best interest and still optimize the
SC, the value of W5 must be chosen such that the right-hand sides of Equations (4.33) and
(4.34) are the same. This happens iff W5 is given by:
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CHAPTER
W5*
E
S
(1 J 5 ) J 5 E B p D S E B E S D B
.
ES EB
4
(4.35)
Using W5* yields the following profit for the SC:
T5 (W5* )
( p D S D B )2
4( E B E S )
–.
(4.36)
It follows that the revenue sharing contract [W5* , J 5 ] optimizes the SC for any value of J 5
(0 < J 5 < 1).Ŷ
To analyze the win-win possibilities of the revenue sharing contract we make the
following observations. By using the wholesale price W5* as given in Equation (4.35), the
Buyer and Supplier profits are given by:
§ EB
B5 (W5* , J 5 ) ¨¨
© EB ES
·
¸¸3 ; and
¹
§ ES
S 5 (W5* , J 5 ) ¨¨
© EB ES
·
¸¸3 .
¹
(4.37)
(4.38)
It is immediately clear from Equation (4.37) and Equation (4.38) that the profits for the
Supplier and the Buyer do not depend on J 5 . In other words, the parameter J 5 does not
influence the profits for the Buyer and the Supplier. In fact, the profit for the Supplier is
lower than that in the solitaire scenario. From the above analysis, we can conclude that
the revenue sharing mechanism does not provide a win-win solution as the players’
profits are independent of the contract parameters. One intuitive explanation for this
disappointing result could be that the marginal revenue for the Buyer is constant (which
was also observed within the Hirshleifler analysis). A result in Cachon (2005) indicates
that the revenue sharing mechanism will not coordinate the SC when the marginal
revenue is constant, which is clearly true in this analysis.
Example (continued)
The results for the numerical example are given in Table 4.3.
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
Scenario
W
Q
B
S
T
0
Centralized
n/a
10
n/a
n/a
300
1
Solitaire
65
7.5
56.25
225
281.25
5
Revenue sharing
60
10
100
200
300
Table 4.3: Revenue sharing results (Numerical example)
It can be observed that the revenue sharing mechanism coordinates the SC (same profit as
in the centralized scenario) but does not provide win-win (Supplier profit is lower than
under the solitaire scenario).Ŷ
In the next section, we analyze the profit sharing mechanism.
4.6
Profit Sharing mechanism
In the profit sharing mechanism (denoted by subscript 6) the transactions between the
Supplier and the Buyer are governed by the Supplier receiving a share of the Buyer’s
profits. Jeuland & Shugan (1983) have used profit sharing as a mechanism to achieve
channel coordination. The profit sharing mechanism can be identified by two parameters,
namely, wholesale price W6 and a percentage of the Buyer’s profit G 6 (0 < G 6 < 1), set by
the Supplier.
Under the profit sharing contract [W6 , G 6 ] , the profit functions are:
S 6 (W6 , Q6 , G 6 ) W6 Q6 G 6 ( p W6 )Q6 D B Q6 E B (Q6 ) 2 D S Q6 E S (Q6 ) 2 (4.39)
for the Supplier;
B6 (W6 , Q6 , G 6 )
(1 G 6 )( p W6 )Q6 D B Q6 E B (Q6 ) 2 (4.40)
for the Buyer; and
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CHAPTER
T6 (Q6 )
S 6 B6
p Q6 (D S D B )Q6 ( E S E B )(Q6 ) 2
4
(4.41)
for the SC.
The performance of the profit sharing mechanism is summarized in Theorem 4.2.
Theorem 4.2
(i)
The Profit sharing contract [W6* , G 6 ] with W6*
ES ( p DB ) DS EB
will lead to a
(E S E B )
coordinated SC for all 0 < G 6 < 1.
(ii)
For any price W1 under the solitaire scenario, there is a value for G 6 and
W6* under the profit sharing contract [W6* , G 6 ] such that both the Supplier and the
Buyer achieve higher profits under the profit sharing scenario than their realized
profits under the solitaire scenario.
Proof
(i) The order quantity which will optimize the Buyer’s profit can be obtained from (4.40)
as:
Q6*
To ensure that Q6*
(4.42)
p W6 D B
.
E B (1 G 6 )
Q0* , it follows from Equations (4.42) and (4.4) that the Buyer orders
the optimal quantity when:
W6*
(4.43)
ES ( p DB ) DS EB
.
ES EB
The optimal wholesale price in Equation (4.43) will yield the following profits:
T6
T6 (W6* )
( p D S D B )2
4( E B E S )
–
(4.44)
for the total SC;
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105
S6
§ E G6 EB
S 6 (W6* , G 6 ) ¨¨ S
© EB ES
·
¸¸ –
¹
(4.45)
B6
§ (1 G 6 ) E B
B6 (W6* , G 6 ) ¨¨
© EB ES
·
¸¸ –
¹
(4.46)
for the Supplier; and
for the Buyer.
It follows immediately from Equation (4.44) that the profit sharing mechanism [W6* , G 6 ]
will optimize the SC for any value G 6 (0 < G 6 < 1).
(ii) It is clear from Equations (4.45)-(4.46) that the profits for the Supplier and the Buyer
are dependent on G 6 . Hence, G 6 can be used to divide the profits between them, in the
“required” proportions. A win-win opportunity is achieved if both the Buyer and the
Supplier earn higher profits with profit sharing as compared to their profits in a solitaire
scenario. The profit for the Supplier under the profit sharing mechanism is greater than
his profit in a solitaire scenario iff:
G6 !
·
1 § ( E S E B ) S1 (W1* )
¨
E S ¸¸ : (G 6 ) .
–
E B ¨©
¹
(4.47)
Furthermore, the profit for the Buyer under the profit sharing mechanism should be
greater than his profit in a solitaire scenario, i.e.,
§ 1 ·§ ( E S E B ) B1 (W1* ) ·
¸¸¨¨
¸¸ : (G 6 ) .
–
E
¹
© B ¹©
G 6 1 ¨¨
(4.48)
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. This follows from:
§ E EB ·
¸¸(– T1 (W1* )) > 0
(G 6 ) (G 6 ) = ¨¨ S
–
E
© B
¹
(4.49)
It follows from Equation (4.14) that the expression in Equation (4.49) will always be
greater than zero. Only in the special case when the realized profit under the solitaire
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4
scenario is equal to the optimal profit will the value of this expression be equal to zero in
which case there are no win-win opportunities. This concludes the proof.Ŷ
Example (continued)
Table 4.4 gives the results for the numerical example.
Scenario
W
Q
G
B
S
T
0
Centralized
n/a
10
n/a
n/a
n/a
300
1
Solitaire
65
7.5
n/a
56.25
225
281.25
6
Profit sharing
60
10
0.4
60
240
300
Table 4.4: Profit sharing results (Numerical example)
Assuming G6 = 0.4, it can be seen that when compared to the solitaire scenario, win-win is
achieved. In fact, this happens iff 0.25 < G6 < 0.4375. Furthermore, it can be seen that
under the profit sharing contract [W6 = 60; G6 = 0.4] the SC is coordinated (T6 = T0).Ŷ
In the next section we discuss the quantity discount mechanism.
4.7
Quantity discount & license fee mechanism
With the quantity discount mechanism (denoted by subscript 7), the Supplier fixes a base
price O7 and charges an additional price which is a decreasing function in Q7 . At its
simplest form, the price at which the seller sells the product to the Buyer is dependent
upon the order quantity and is given by:
W7 (Q7 ) O7 P7
Q7
.
(4.50)
Using the wholesale price function in Equation (4.50) yields the following profits:
S 7 (O7 , P 7 , Q7 ) (O7 D S )Q7 E S (Q7 ) 2 P 7
(4.51)
for the Supplier;
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B7 (O7 , P 7 , Q7 )
( p O7 D B )Q7 E B (Q7 ) 2 P 7
107
(4.52)
for the Buyer; and
T7 (Q7 ) ( p D S D B )Q7 ( E S E B )(Q7 ) 2
(4.53)
for the SC. Note that the SC profit as given in Equation (4.53) is independent of the
parameters of quantity discounts.
The following theorem explains the ability of the quantity discount mechanism to provide
coordination and win-win opportunities.
Theorem 4.3
(i)
The quantity discount contract [O*7 , P 7 ] with O*7
ES p DS EB DBES
leads to a
(E S E B )
coordinated SC for all P 7 .
(ii)
For any wholesale price W1 under the solitaire scenario, there is a quantity
discount contract [O*7 , P 7 ] such that both the Supplier and the Buyer earn higher
profits under the quantity discount scenario than the realized profits under the
solitaire scenario.
Proof
(i) The order size Q7 which will optimize the profit for the Buyer can be obtained from
Equation (4.54) as:
Q7*
To ensure that Q7*
p O7 D B
.
2E B
(4.54)
Q0* , it follows from Equations (4.54) and (4.4) that the Buyer orders
the SC optimal quantity when:
O*7
ES p DS EB DBES
.
(E S E B )
(4.55)
Substituting this value of O*7 in (4.53)-(4.55) yields the following profits:
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CHAPTER
T7
( p D S D B )2
4( E B E S )
–
4
(4.56)
for the SC;
§ ES
S 7 ( P 7 ) ¨¨
© EB ES
·
¸¸ – P 7
¹
(4.57)
§ EB
B7 ( P 7 ) ¨¨
© EB ES
·
¸¸ – P 7
¹
(4.58)
for the Supplier; and
for the Buyer.
From Equation (4.56) it follows immediately that the quantity discount contract [O*7 , P 7 ]
coordinates the SC for all values of P 7 .
(ii) Win-win is achieved if the profit with quantity discount is higher than the profit in a
solitaire scenario. The profit for the Buyer with quantity discount should be greater than
his profit in a solitaire scenario, i.e.,
§ EB
P7 ¨¨
© EB ES
·
¸¸ – S1 (W1 ) : ( P7 ) .
¹
(4.59)
Furthermore, the profit for the Supplier with the quantity discount should be greater than
his profit in a solitaire scenario, i.e.,
§ EB
P7 ! B1 (W1 ) ¨¨
© EB ES
·
¸¸ – : ( P7 ) .
¹
(4.60)
The proof of the theorem is completed when the difference between the upper and the
lower bounds obtained in Equations (4.61) and (4.62) is positive. This follows from:
( P7 ) ( P7 ) Inside_proefschrift_Vijayender_06.indd 108
– [ B1 (W1 ) S1 (W1 )] t 0
(4.61)
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH INCREASING MARGINAL COST
Clearly, the value in Equation (4.61) will always be positive. It will be equal to zero only
when the SC profit in the solitaire scenario is optimal in which case there are no win-win
opportunities. This concludes the proof.Ŷ
Example (continued)
The results for the numerical example are summarized in the Table 4.5.
Scenario
W
Q
O
P
B
S
T
0
Centralized
n/a
10
n/a
n/a
n/a
n/a
300
1
Solitaire
65
7.5
n/a
n/a
56.25
225
281.25
7
Quantity discount
n/a
10
60
30
70
230
300
Table 4.5: Quantity discount results (Numerical example)
Assuming P7*
30 , it can be seen that when compared to the solitaire scenario, win-win
is achieved. In fact, this happens iff 25 < P 7* < 43.75. Furthermore, it can be seen that
under the quantity discount contract [O*7
60; P 7
30] the SC is coordinated (T7 = T0).Ŷ
With a license fee contract the Supplier gets a fixed amount L8 in addition to the price
W8 per item. The license fee mechanism is also called a two-part tariff mechanism. It is
easy to see that a license fee contract [W8* , L8 ] has exactly the same effect as the quantity
discount contract [O*7 , P 7 ] if P 7
L8 and O*7
W8* .
In the next section we conclude our study.
4.8
Conclusions
When the Buyer and the Supplier incur costs which are quadratic functions of the ordered
quantities, the intra-firm transfer pricing mechanisms suggested in the literature are not
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4
applicable in a SC setting since they do not provide coordination and win-win
opportunities between autonomous entities at the same time.
Four contract mechanisms, namely the revenue sharing, profit sharing, quantity discount
and license fee mechanisms are designed. Our analysis shows that the revenue sharing
mechanism coordinates the SC but does not provide win-win opportunities. Profit
sharing, quantity discounts and the license fee mechanisms are shown to coordinate the
SC and provide win-win opportunities.
This study offers scope for further research as well. One extension would be to make the
final selling price a decision variable and make the end-consumer demand dependent on
price. It would be interesting to study the performance of the revenue sharing mechanism
in such a setting. Information asymmetry can also be introduced into this setting, i.e.,
each player does not know the cost functions of the other with certainty. Other possible
extensions include introducing competition at the Buyer and/or Supplier level.
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111
Chapter 5
Coordinating Pricing and Replenishment Decisions in a Supply Chain
with Two Consumer Segments 5
Chapter Synopsis
In this chapter, the issue of coordinating pricing and replenishment decisions in a supply
chain (SC) where the end-consumers are comprised of two segments is discussed. It is
assumed that one consumer-segment has a high willingness-to-pay and the second has a
low willingness-to-pay. In this setting, it is shown that the direct rebate mechanism (mailin-rebate) as suggested by Gerstner & Hess (1991, 1995), does not coordinate the SC for
all parameter values. To overcome this drawback, we design revenue and profit sharing
mechanisms and show that both these mechanisms can coordinate and provide win-win
opportunities for all parameter values. We also establish an equivalence relationship
between the revenue and profit sharing mechanisms.
5.1
Introduction
Price differentiation among different customer segments is a very well-known practice in
industries such as the airlines, hotels, car rentals, et cetera. Different price/service
combinations are used to create barriers among different customer segments. This issue is
addressed in the revenue management literature in great detail. More recently, revenue
management principles have also been used by product based companies such as Dell. In
fact, Dell’s success with differentiated and dynamic pricing practice can be attributed to
its unique SC design and also its use of the internet as its predominant selling channel.
However, it is not always feasible to price-differentiate and create barriers among
5
This Chapter is a revised, updated and elaborated version of the paper presented at POMS 2006
conference in Boston [Reference: Nalla, V. R, J.A.A van der Veen, and V. Venugopal (2006a)].
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5
different consumer segments. For example, consider the case of a consumer electronics
retailer selling camcorders in a retail store. It is very likely that customers with different
willingness-to-pay would arrive at the same retail store. In a situation like this, the retailer
could try to maximize his own profit by selling the low-end product only to the high
willingness-to-pay customer segment, even though selling to both segments might be a
more profitable option for the entire SC. This chapter designs mechanisms which can
coordinate such a SC. In this setting, the manufacturer’s and retailer’s self-interested
marketing decisions might be the cause for SC inefficiency, an issue which in the
literature is commonly addressed and understood as double marginalization (see e.g.,
Spengler (1950) and Van der Veen & Venugopal (2000)).
In this chapter the same setting is considered as in Gerstner & Hess (1991, 1995). In these
papers the authors design a direct rebate mechanism (manufacturer offers discounts
directly to consumer) and call this mechanism the pull discount mechanism. They show
that the direct rebate mechanism performs better than the decentralized channel and
coordinates the SC for a greater range of parameter values. However, we will
demonstrate that the direct rebate mechanism does not coordinate the SC for all
parameter values. To overcome this drawback, we design a revenue and a profit sharing
mechanism and show that these mechanisms do coordinate the SC for all parameter
values and, moreover, provide win-win opportunities under appropriate parameter
settings.
The remainder of this chapter is organized as follows. In the next section, we present our
model and discuss the performance of the centralized and the decentralized scenario.
Subsequently, we analyze the pull discount mechanism and show its shortcomings. This
is followed by a discussion of SC contracts, and we demonstrate that these mechanisms
overcome the shortcomings of the pull discount mechanism. We end with conclusions
and managerial insights gathered from this study.
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5.2
Model and Basic Analysis
Q
Supplier
Supplier
Q
WW
Q
Buyer
Buyer
High
consumers
Highwillingness
willingness
consumersph h
p
α Į
pp
Low
consumers
LowWillingness
Willingness
consumersp l
PL !DpPlH
(1-α)
(1-Į)
Figure 5.1: Model with two different consumer segments
Figure 5.1 shows a situation in which a Supplier distributes a single product through an
exclusive independent Buyer. The Buyer sets the final selling price to maximize his
profit, and the Supplier decides on the wholesale price. For simplicity, the Supplier’s
costs are assumed to be zero. It is also assumed that both the Supplier and the Buyer have
symmetric and complete information.
Two consumer segments make up the market: high willingness-to-pay consumers (Highs
for short) and low willingness-to-pay consumers (Lows). The Highs place a reservation
price ph on the product, and the Lows have a reservation price pl , where 0 pl p h .
The product is sold by the Supplier to the Buyer at a wholesale price W , and the Buyer
resells the product at a final selling price as determined by the Buyer. It is convenient to
normalize the size of the market to 1. Let D be the segment size of the Highs and (1 D )
be the segment size of the Lows.
First consider the centralized scenario, i.e., the situation in which the Supplier and the
Buyer operate as a single unit and work jointly to optimize SC profit. Basically, the SC
has two options: (1) Sell the product to all customers at price pl ; or (2) sell the product
only to the Highs at price p h . The SC profits in these two situations are pl and Dp h
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5
respectively. It can be concluded that the centralized SC would opt for serving the entire
market iff pl t Dp h .
Next we consider a decentralized scenario in which both the Buyer and the Supplier are
interested in maximizing their own profits (in this scenario the decision variables will be
indicated with a subscript 1).
Under the decentralized scenario, the Buyer has two options:
Option 1:
Sell to Highs only. In this case the profit for the Buyer is equal to
D ( p h W1 ) .
Option 2:
Sell to both the segments. Here the profit for the Buyer is pl W1 .
It follows that, for any given W1 , the Buyer will decide to sell to both the segments iff:
W1 d
pl Dp h
.
1D
(5.1)
The Supplier’s profit is given by DW1 if the Buyer decides to sell to the Highs only and
W1 if the Buyer decides to sell to both segments. Also the Supplier has two options:
Option 1:
Fix the wholesale price W1*
p h . In this case the Buyer will sell to the
Highs only. The profits for the Supplier, Buyer and the SC can therefore be
Dp h ; B
obtained as: S
Option 2:
S B Dp h .
0 ;T
Fix the wholesale price W1*
p l Dp h
. In this case the Buyer will sell to
1D
both segments, so that the profits for the Supplier, Buyer and the SC can be
obtained as:
p l Dp h
;
1D
(5.2)
D ( p h pl )
; and
1D
(5.3)
S
B
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH TWO CONSUMER SEGMENTS
SB
T
115
(5.4)
pl
respectively.
It can be concluded that the Supplier will choose Option 2 iff the profit in Equation (5.2)
is greater than Dp H , i.e., when:
pl ! D (2 D ) ph .
(5.5)
The above analysis leads to the following conclusion:
If pl ! D (2 D ) ph , then
W1*
T
If pl d D (2 D ) ph , then
W1*
( p l Dp h )
;S
(1 D )
( p l Dp h )
;B
(1 D )
D ( p h pl )
;
(1 D )
pl (sell to both the segments).
ph ; S
Dp h ; B 0 ; T
Dp h (sell only to Highs).
Recall that a centralized channel will sell to both segments when pl ! Dph . It can be
concluded that double marginalization occurs when:
Dp h p l Dp h ( 2 D ) .
(5.6)
In the literature (see Gerstner & Hess (1991, 1995)), this interval is referred to as the
breakdown region. To provide some additional insight into the above result, pl is
represented along a one-dimensional axis and the behavior of the supply chain for
different values of pl is depicted in Figure 5.2.
From Figure 5.2 it is clear that when pl Dp h , the centralized SC and the decentralized
channel will sell only to the Highs, and the total SC profit in both cases is Dp h . When
pl ! D (2 D ) p h both the centralized and the decentralized channel will sell to all
consumers and the SC profit will be pl . However, when Dp h pl D (2 D ) p h , the
centralized SC will sell to both the segments, and the SC profit is pl . Furthermore, the
decentralized channel will sell only to Highs, and the SC profit remains Dp h .
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CHAPTER
T
Dp h
T
5
pl
Sell to all
Sell to Highs only
pl
Centralized channel
Sell to Highs only
Sell to all
pl
Decentralized channel
T
Dp h
S
Dp h
B
0
T
Centralized and decentralized sell to Highs only
Double marginalization
Dp h
pl
S
( pl Dph )
(1 D )
B
D ( ph pl )
(1 D )
Centralized and decentralized sell to all
D ( 2 D ) ph
Figure 5.2: SC performance for different parameter values
Note that in this case the decentralized channel makes a lower profit as compared to the
centralized channel. In other words, in this breakdown region, the SC profit is lowered by
a lack of coordination between the players. It is the objective of this chapter to design
mechanisms which will coordinate the SC also for this breakdown region.
Example
The following numerical example will be used throughout this chapter to illustrate the
results. The willingness-to-pay for Highs is considered to be €3.00 and the Highs segment
size is Į = 0.6. The Lows willingness-to-pay pl is assumed to be €2.00.
With these parameter values the double marginalization phenomena can be observed in
the breakdown region 1.8 pl 2.5 . In this case the Buyer will sell to both segments
when the wholesale price is less than or equal to €0.5. However, at any wholesale price
the Supplier fixes in this range, he earns a lower profit than when he fixes the wholesale
price at €3.00. When the Supplier fixes the wholesale price at €3.00, the Buyer will sell
only to the highs and the total SC profit will be €1.80, which is lower than the centralized
SC profit of €2.00. These results are depicted in Figure 5.3.Ŷ
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH TWO CONSUMER SEGMENTS
p l ,Profits
Profits
p = 3, α = 0.6
p lP= 2,
L = 2, hPH = 3, Į = 0.6
w
p
PL =l =2 2
α ph =
w
Supply
Chain
Supply
Chain
αW
ĮPH = 1.8
ĮW
Supplier
Supplies
0.5
0.5
Į(PH – W)
α(p h – W)
Buyer
( p l – W)
0.5
W=
0.5
( pl −α ph)
Buyer
W
PL – W)
ph
(1 − α )
(PL DPH )
W
(1 D)
W
3
PH
Figure 5.3: Profit for the players and the supply chain in a decentralized scenario
To overcome the issue of double marginalization, several contract mechanisms are
proposed. We will review such mechanisms below and discuss their ability to provide
coordination and win-win opportunities. We first design and discuss the direct rebate
mechanism and later discuss the revenue and profit sharing mechanisms.
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5.3
5
Direct rebate as coordination mechanism
In a direct rebate mechanism, the Supplier offers discounts directly to the price-conscious
consumers, expecting them to obtain the product from the Buyer; see e.g., Gerstner &
Hess (1991, 1995).
The use of discounts to consumers can be modeled as follows. It is assumed that a
consumer must exert some effort to obtain the direct rebate, and this effort has a
monetary equivalent called the transaction cost. If the direct rebate exceeds the
transaction cost, the consumer uses the discount. For simplicity the Low’s transaction
cost is normalized to zero, and the High’s transaction cost is denoted by z. That is,
z should be interpreted as the transaction cost differential between the Highs and the
Lows.
First we shortly review the direct rebate mechanism as given in Gerstner & Hess (1995,
1991). In their study, Gerstner & Hess call these direct rebates “pull discount
mechanisms”. With the direct rebate mechanism, the wholesale price is at the same level
as in the decentralized scenario, i.e., W2
p h (where W2 is the wholesale price with the
pull discount mechanism). The following sequence of events takes place under the direct
rebate mechanism:
1) The Supplier fixes the wholesale price as in the decentralized scenario: W2*
ph ;
2) The Supplier offers consumers a direct rebate of D2 ;
3) The Highs incur a transaction cost of z to use the discount;
4) The Buyer calculates that the Highs would be willing to pay a price of p h D2 z ,
and that the Lows would be willing to pay pl D2 , taking the discount into account;
5) The Buyer decides on the final selling price.
Clearly in this situation the Buyer has two options to consider:
Option 1:
Sell to the Highs only at a price p h D2 z .
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH TWO CONSUMER SEGMENTS
Under this option the profit for the Buyer can be obtained as D ( D2 z ) .
Sell to both segments at price pl D2 .
Option 2:
In this case the profit for the Buyer can be obtained as ( pl D2 ) p h .
The Buyer will decide to sell to both segments iff:
D2 t
( p h p L ) Dz
.
1D
(5.7)
Furthermore, the Supplier’s Profit is given by D (W2* D2 ) if the Buyer decides to sell to
Highs only, and p h D2 if the Buyer decides to sell to both segments.
Also the Supplier has two options:
Option 1: Fix the direct rebate at D2*
( p h p l ) Dz
1D
and the wholesale price at W2*
ph .
The Buyer will sell to both segments.
The Profits for the Supplier, Buyer and the SC can be obtained as:
S2
pl D ( p h z )
; B2
1D
D ( p h pl ) Dz
;T
1D
Option 2: Fix the direct rebate value D2*
0 so that S
pl respectively.
Dp h ; B 0 ; T Dp l .
Obviously, the Supplier prefers Option 1 (sell to both segments) when it results in a
higher profit to him when compared to Option 2, i.e., iff:
pl Dph (2 D ) Dz .
(5.8)
It can be concluded that under the direct rebate mechanism, the breakdown region is
given by the interval Dp h pl D (2 D ) p h Dz . Clearly, when compared to the
breakdown region in the decentralized scenario, this is a reduction. In fact, if
z
(1 D ) ph , the double marginalization is completely eliminated. At the other side of
the spectrum, if z
0 then the direct rebate mechanism’s performance is the same as that
of the decentralized scenario. Any value of z between 0 and (1 D ) ph will reduce the
double marginalization range when compared to the decentralization scenario.
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Note that within the interval that is defined by the difference of the breakdown regions,
both the Buyer and the Supplier make greater profits than in the decentralized channel. It
can therefore be concluded that the direct rebate mechanism provides coordination for a
greater range of parameter values and also provides win-win opportunities in the
improved region. The results of the direct rebate mechanism are summarized in Figure
5.4.
T
Dp h
T
pl
Sell to all
Sell to Highs only
pl
Centralized channel
Sell to Highs only
Sell to all
pl
Direct rebate
T
Dp h
S
Dp h
B
0
Centralized and decentralized sell to Highs only
T
S
Double
marginalization
Dp h
B
T
pl
( pl D ( ph z )
]
(1 D )
(D ( ph pl ) Dz )
(1 D )
pl d Dph (2 D ) Dz
pl
S
( pl Dph )
(1 D )
B
D ( ph pl )
(1 D )
Centralized and decentralized sell to all
D ( 2 D ) ph
Figure 5.4: The double marginalization range for the direct rebate mechanism
As can be seen from Figure 5.4, the direct rebate mechanism coordinates the SC and
products are sold to both the segments when pl ! Dph (2 D ) Dz . A win-win
opportunity is achieved in the region where the direct rebate mechanism coordinates and
the decentralized channel does not. The profits for the Supplier and the Buyer in the
additional coordinated region are
pl D ( p h z )
D ( p h p l ) Dz
and
, which are greater
1D
1D
than the profits they make in the decentralized scenario.
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121
Example (continued)
For the numerical example and for a z value of 0.85, the profits for the Supplier, Buyer
and the SC are 1.85, 0.15 and 2 respectively. For a z value of 0.85, both coordination and
win-win opportunities are achieved.Ŷ
5.3.1
Push-pull discounts
Recall that under the direct rebate mechanism the Supplier’s wholesale price was
assumed to be equal to his wholesale price under the decentralized scenario. The
motivation for that assumption is that typically rebates are used for promotional purposes,
and since a promotion is usually only for a limited period, the base-case scenario is the
decentralized scenario. In other words, the decision on the rebate value is taken under the
assumption that the wholesale price was set earlier, hence is a known value.
Clearly, it is also interesting to see what happens if this assumption is relaxed. That is:
how would the Supplier behave in case he can jointly decide on his wholesale price and
his rebate value, and what would be the impact on the SC performance? In fact, Gerstner
& Hess (1995, 1991) have analyzed such a situation and named the associated
mechanism push-pull discounts. Here we do not discuss these results in detail for the
simple reason that with this chapter we have a different objective, namely to show that
coordination can be achieved without rebate discounts, namely through the revenue
sharing mechanism or profit sharing mechanism. However, it is worthwhile to mention
one important aspect of the Gerstner & Hess (1995, 1991) push-pull discount model,
namely the fact that additional SC profit can be obtained from the fact that the Highs face
transaction costs z. As will be shown below, this does have an impact on the optimal
decisions and the rebate value.
Let us review the centralized SC situation. Before it was shown that the centralized SC
would decided to sell to all consumers iff pl t Dph . However, at that analysis the
transaction costs of the Highs at a rebate were not taken into account. Therefore, now
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5
assume that besides setting a price P to the end-consumers, the centralized channel can
also simultaneously determine a rebate value D offered to all consumers. Again the
transaction costs of the Highs are denoted by z and it is assumed that the Lows do not
face any transaction costs. It follows that the willingness-to-pay for the Lows is pl D .
The willingness-to-pay of the Highs is p h if D ” z and p h ( D z ) if D • z. The
centralized SC has two options:
(1) Sell to all consumers at price pl D , in which case the SC profit would be
( pl D) (1 D ) D
pl DD if D ” z and ( pl D) D
the optimal rebate value is D *
pl if D • z. It follows that
z and the associated profit in this option is pl Dz .
(2) Sell to the Highs only. The SC profit in this case is ph if D ” z and
( p h ( D z )) D D ( p h z ) if D • z. Clearly under this option D *
0 and the SC
profit is Dp h .
It can be concluded that the centralized SC would decide to sell to all if pl ! D ( ph z ) .
If this is the case, the wholesale price is set at pl z and the rebate value at z. Note that
under this assumption and when compared to the situation as discussed in Section 5.2, the
wholesale price and the rebate value both are increased by z (earlier the rebate value was
not included, i.e., equal to 0). As a result the SC profit is increased by Dz . Clearly, the
difference between the situation discussed here and the original analysis (as discussed in
Section 5.2) can entirely be contributed to the assumption that the Highs have a
transaction cost z > 0. In case z = 0, the two situations are exactly the same.
In fact it is easy to show that if it is allowed to simultaneously decide on the wholesale
price and the rebate value, in order to capture this additional SC profit, it is always
possible to use an optimal rebate value of z. This holds for the centralized channel (as
demonstrated above), but also for the decentralized channel, for the rebate mechanisms
and also for the mechanisms discussed below (revenue sharing and profit sharing). To be
more precise, if these mechanisms are combined with a rebate at value z, the results fully
correspond to the situations without a transaction cost and without a rebate possibility.
For this reason, it is superfluous to include the possibility to offer a rebate on top of other
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123
mechanisms in our analysis. It is for this reason that we refrain from a further analysis of
the push-pull discount.
In the next section we discuss the revenue sharing mechanism.
5.4
Revenue sharing
In the revenue sharing mechanism, the transactions between the Supplier and Buyer are
governed by the Supplier receiving a share of the Buyer’s revenues. The revenue sharing
mechanism [W3 , J 3 ] can be identified by two parameters, namely, wholesale price W3
and a percentage of the Buyer’s profit J3 (0 < J3 <1) that goes to the Supplier (where the
subscript 3 refers to the revenue sharing scenario). Many supply contracts in vertically
separated industries include revenue sharing. One recent example is from the
videocassette rental industry; see Cachon & Lariviere (2005), Dana & Spier (2001).
The following theorem explains the ability of the revenue sharing mechanism to provide
coordination and win-win opportunities.
Theorem 5.1
If Dp h pl Dp h (2 D ) , then there is a revenue sharing contract [W3* , J 3 ] such that
(i)
the Supply Chain is coordinated;
(ii)
the Buyer and Supplier achieve higher profits under the revenue sharing contract
when compared to the solitaire scenario.
Proof
(i) Basically, the Buyer has two options:
Option 1:
Sell to Highs only. In this case the profit for the Buyer can be obtained as:
D ( p h W3 ) J 3 Dp h .
Option 2:
Sell to both segments. Under this option, the profit for the Buyer is given
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5
by: (1 J 3 ) pl W3 .
It follows that for any given contract [W3 , J 3 ] the Buyer will decide to sell to both
segments iff:
§ p Dp h
W3 d (1 J 3 )¨ l
© 1D
·
¸.
¹
(5.9)
§ p Dp h ·
Now consider a revenue sharing contract with W3* : (1 J 3 )¨ l
¸ . Since the Buyer
© 1D ¹
will decide to sell to all segments, the profit for the Buyer is given by:
B3
§ D ( p h pl ) ·
(1 J 3 )¨
¸.
© 1D
¹
(5.10)
The Supplier’s profit is given by:
S3
pl (1 J 3D ) Dp h (1 J 3 )
.
1D
(5.11)
It follows that the total SC profit T3 = B3 + S3 = pl ; i.e., the SC is coordinated for all
0 < J3 <1.
(ii) To ensure win-win opportunities, the profits for both players must be greater than
what they achieve in a solitaire scenario. The Supplier’s profit under the revenue sharing
contract [W3* , J 3 ] is larger than the profit he obtains in the solitaire scenario iff:
pl (1 J 3D ) Dph (J 3 1)
! Dp h ,
1D
which gives a lower bound for J 3 as:
J3 !
D (2 D ) ph pl
D ( ph pl )
(J 3 ) .
(5.12)
The Buyer’s profit under the revenue sharing contract [W3* , J 3 ] is higher than the profit
he obtains in the solitaire scenario iff:
§ D ( ph pl ) ·
(1 J 3 )¨
¸ ! 0,
© 1D ¹
which gives a upper bound for Ȗ3 as:
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J 3 1 (J 3 ) .
125
(5.13)
To get the desired result it remains to be shown that J 3 J 3 ! 0 . This follows
immediately from:
J 3 J 3
(1 D )( pl Dph )
! 0.
D ( p h pl )
(5.14)
The condition in Equation (5.14) is valid since pl ! Dph under the assumption in the
theorem.Ŷ
Example (continued)
For our numerical example, the wholesale price can be obtained from Equation (5.9) as
W3*
0.5(1 J 3 ) . The Supplier’s profit from Equation (5.11) is (0.5 1.5J 3 ) and the
Buyer’s profit from Equation (5.10) is (1 J 3 ) . The lower bound for J 3 is obtained from
Equation (5.12) as 0.87 and the upper bound using Equation (5.13) is 1. To illustrate,
these results are depicted in Figure 5.5. Ŷ
5.5
Profit sharing
In the profit sharing mechanism, the transactions between the Supplier and the Buyer are
governed by the Supplier receiving a share of the Buyer’s profits. Jeuland & Shugan
(1983) have used profit sharing as a mechanism to achieve SC coordination. The profit
sharing mechanism [W4 , G 4 ] can be identified by two parameters, namely, wholesale
price W4 and a percentage of the Buyer’s profit G 4 (0 < G 4 < 1) that goes to the Supplier
(where subscript 4 refers to the profit sharing scenario) .
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5
p l , Profits
SC Profit – Revenue Sharing
pl = 2
Supplier – Revenue Sharing
Supplier – Solitaire
α p h = 1.5
(1 -γ )[
( pl - α ph)
] = 0.5
1- α
Buyer – Revenue Sharing
γ-
γ +=1
γ
Region for γ to
achieve win-win
c eve w
w
Figure 5.5 Profit profiles for players and the supply chain for
different revenue share percentages
The following theorem establishes the equivalence of the profit and revenue sharing
contracts.
Theorem 5.2
If J 3
G 4 then the revenue sharing contract [W3*
sharing contract [W4*
§ p l Dp h
¨
© 1D
§1 J 3
¨¨
© 1D
·
¸¸( pl Dp h ); J 3 ] and the profit
¹
·
¸; G 4 ] result in the same profits for the Buyer, Supplier
¹
and SC.
Proof
Under the profit sharing mechanism, the Buyer has two options:
Option 1:
Sell to the Highs only. In this case the profit for the Buyer is equal to:
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SUPPLY CHAIN WITH TWO CONSUMER SEGMENTS
(1 G 4 )D ( ph W4 ) .
Option 2:
Sell to both segments. The profit for the Buyer under this option
can be obtained as: (1 G 4 )( pl W4 ) .
For any given contract [W4 , G 4 ] the Buyer will decide to sell to both the segments iff
W4 d
pl Dp h
.
1D
Now consider a profit sharing contract with W4* :
(5.15)
p l Dp h
. Since the Buyer will decide
1D
to sell to all the segments, the profit for the Buyer is given by:
B4
§ D ( p h pl ) ·
(1 G 4 )¨
¸.
© 1D
¹
(5.16)
The Supplier’s profit is given by:
S4
pl (1 G 4 D ) Dp h (1 G 4 )
.
1D
From Equations (5.10) and (5.16) it is clear that if J 3
from Equations (5.11) and (5.17) it follows that if J 3
implies that if J 3
(5.17)
G 4 , then B3 = B4. Furthermore,
G 4 , then S3 = S4 . Clearly this also
G 4 , then T3 = T4.Ŷ
The following result summarizes the key results of the profit sharing mechanism.
Corollary 5.3
If Dp h pl Dp h (2 D ) , then there is a profit sharing contract [W4* , G 4 ] such that:
(i)
the Supply Chain is coordinated
(ii)
the Buyer and Supplier achieve higher profits under the revenue sharing contract
when compared to the solitaire scenario.
Proof
Follows directly from Theorems 5.1 and 5.2. Ŷ
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5.6
CHAPTER
5
Conclusions
This chapter finds its roots in Gerstner & Hess (1995, 1991). In these papers, a SC model
with two consumer segments, each with their own willingness-to-pay is introduced. If the
pricing decisions are decentralized this leads to a sub-optimal situation, a phenomenon
known as double marginalization. Gerstner & Hess (1995, 1991) was focused on rebate
mechanisms to overcome the double marginalization issue. One of their results
(reproduced in Section 5.3) was that the direct rebate mechanism coordinates the SC for a
greater range of parameter values as compared to the decentralized channel. However,
this mechanism does not coordinate the SC for all parameter values. This chapter adds to
the literature by showing that the revenue and profit sharing mechanisms do coordinate
the SC for all parameter values. Moreover, it is demonstrated that the revenue sharing and
profit sharing mechanisms are capable of providing win-win opportunities. Furthermore,
an equivalence relationship between the revenue and profit sharing mechanisms is
established.
This study offers some scope for further research. One possible extension is to add a
dimension of uncertainty to the willingness-to-pay of different consumer segments. The
introduction of information asymmetry, for example only the Buyer knows the effect of
service on the end-consumer demand with certainty, is another possible extension.
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129
Chapter 6
Coordinating Pricing and Replenishment Decisions in a SC with
Uncertain Demand 6
Chapter Synopsis
This chapter deals with the pricing and the replenishment decisions in a two-echelon
Supply Chain (SC) in which the end-consumer demand is uncertain. We study the effect
of various coordination mechanisms such as profit sharing, revenue sharing, two-part
tariff (license fee) and buy-back in the given setting. We mathematically prove that a
win-win situation (in terms of expected profit) exists in the chosen setting for the chosen
coordination mechanisms. We discuss the risk and the reward sharing with each of the
contract mechanism with the help of a numerical example. These results can be used in
practice as a “convincing tool” to get the commitment of the SC players in the process of
implementing coordination mechanisms.
6.1
Introduction
In this chapter, we consider a setting where the end-consumer demand is uncertain. More
precisely, it is assumed that the players in the SC do not know the exact demand but they
are aware of the probability distribution of demand.
Clearly, when the demand follows a probability distribution, there is a possibility for the
demand to be greater than the stocked/produced quantities (stock-out) or it can also be
less than the stocked quantity (left-over). Obviously, both a stock-out and a left-over are
not desirable. In case of a stock-out, the SC looses potential customers and incurs an
6
This chapter is an updated and modified version of the Nyenrode working paper [Reference: J.A.A. van
der Veen & V. Venugopal (2001)].
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6
opportunity cost, whereas when there is a left-over, the SC faces uncovered cost of the
non-sold items. Therefore, it is not a surprise that in such a situation the Buyer orders less
than what is optimal for the SC as a whole.
In the operations and SCM literature, the problem faced by the Buyer in determining his
optimal order quantity problem is known as the Newsvendor problem. More specifically,
the Newsvendor problem is concerned with determining the order quantity that
maximizes the Buyer’s expected profit in a single-period, probabilistic demand setting. In
the Newsvendor model, the Buyer facing an uncertain demand orders a single product
from the Supplier well in advance of a selling season. The Supplier produces after
receiving the Buyer’s order and delivers her production to the Buyer at the start of the
selling season. The Buyer has no additional replenishment opportunity. How much the
Buyer chooses to order depends on the terms of trade between the Buyer and the
Supplier.
In this chapter we take up such a setting and analyze it from a SC perspective. The
remainder of this chapter is organized as follows. First, it is shown that in a decentralized
channel the Buyer orders a lower quantity and the SC profit is lower when compared to
the centralized channel. Subsequently, various contract mechanisms such as the revenue
sharing, profit sharing, license fee, and buy-back are analyzed in a newsvendor setting
and tested for their capability of providing coordination and win-win opportunities. The
chapter is closed with some conclusions.
6.2
Model and Basic Analysis
Consider a SC setting where the end-consumer demand (denoted by D ) is a random
variable following a specified probability distribution f D ( D) , see Figure 6.1. It is
assumed that the product has a short life cycle and hence there is only a one-time order
from the Buyer. Furthermore, it is assumed that the Supplier has infinite capacity and any
unmet demand is lost for the Buyer as reordering is not possible. Moreover, since the
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
product has a short life cycle there is no stock from previous periods, and any unused
stock from previous periods cannot be used.
Supplier
Decides W
C
O
N
S
U
M
E
R
S
Buyer
Decides Q
D
fD
Figure 6.1: A simple SC
It is assumed that the following sequence of events is taking place within the SC:
1. The Supplier sets a wholesale price W per unit knowing that his marginal cost per
unit is c (a constant, independent of number of units produced);
2. Given W and the demand distribution f D ( D) , the Buyer decides his order quantity
and orders Q units from the Supplier;
3. The Supplier ships Q units to the Buyer;
4. Consumer demand D occurs;
5. The Buyer sells the product to the consumers at a fixed retail price of p per unit.
Because of the stochastic demand, the Buyer may encounter two situations: namely that
demand is larger than the Buyer’s order quantity (stock-out; D • Q), or demand is smaller
than the Buyer’s order quantity (left-over; D ” Q). Table 6.1 shows the expected profit of
the Supplier (S), the Buyer (B) and the Supply Chain (T) in the two situations.
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CHAPTER
Situation
Supplier profit
Buyer profit
SC profit
DtQ
(W c)Q
( p W )Q
( p c)Q
DQ
(W c)Q
pD WQ
pD cQ
6
Table 6.1: Expected profits in the wholesale price scenario
The expected profit for the Supplier can be obtained as:
S W , Q W c Q
.
(6.1)
The expected profit of the Buyer is given by:
B (W , Q)
f
Q
Q
0
³ ( p W )Q f D ( D)dD ³ ( pD WQ) f D ( D)dD .
Defining
Q
FD Q :
³f
D
( D)dD,
(6.2)
0
and
GD Q :
Q
³D˜ f
D
( D)dD,.
(6.3)
0
the Buyer’s expected profit can be rewritten as:
B W , Q p W Q p ˜ Q ˜ FD Q p ˜ GD (Q) .
(6.4)
It follows that the expected profit for the SC is given by:
T Q p c Q p.Q ˜ FD Q p ˜ GD (Q) .
(6.5)
Under the centralized scenario (which is denoted by subscript 0) the SC profit given in
Equation (6.5) will be optimized. In fact, the SC is facing the well-known Newsvendor
problem where the per-unit cost of overstocking (item produced but cannot be sold) in the
centralized scenario is represented by c given by c c and the per-unit cost of under-stocking is
p c , i.e., equal to the opportunity cost (profit if an additional unit would
have been available). It follows that SC optimal order quantity is given by:
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
§ c
Q0* : ( FD ) 1 ¨¨ ©c c
·
¸¸
¹
§ pc·
¸¸ .
( FD ) 1 ¨¨
© p ¹
133
(6.6)
The associated SC profit is given by:
p.G D (Q0* ) : – .
T0 (Q0* )
(6.7)
Now consider the so-called solitaire scenario (which is denoted by a subscript 1), in
which it is assumed that there is no cooperation, i.e., the Supplier and the Buyer will act
independently and take decisions that maximize their respective profits. In the solitairescenario, the Supplier first sets his price W1 . Then, the Buyer facing wholesale price W1 ,
consumer price p and demand function f D ( D) , places an order of size Q1 which will
maximize his profits.
Under the solitaire scenario let us first consider the situation of the Buyer. For any
wholesale price W1 , he likes to choose Q1 such that his expected profit is maximized.
Clearly, the Buyer is facing a Newsvendor problem where the per-unit cost of overstocking is given by c under-stocking is c W1 (item bought that cannot be sold) and the per-unit cost of
p W1 ,
i.e., the opportunity cost. It follows that the Buyer’s
optimal order quantity is given by:
Q1* (W1 )
§ c
( FD ) 1 ¨¨ ©c c
·
¸¸
¹
§ p W1
( FD ) 1 ¨¨
© p
·
¸¸.
¹
(6.8)
Assuming that the Buyer uses his optimal order quantity, the profit for the Supplier,
Buyer, and SC are given by:
S1 W1
B1 W1 T1 W1
W
S1 W1 , Q1* W1
p ˜ GD Q1* W1
W
T1 Q1* W1
1
1
c Q1* W1 ;
; and
(6.9)
(6.10)
c Q1* W1 p ˜ G D Q1* W1
(6.11)
respectively. Note that the Buyer’s optimal order quantity and all profits (6.9)-(6.11) do
depend on the wholesale price W1 . This holds in particular for the SC profit. This implies
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6
that W1 is not only used for dividing the overall profit, but also influences the size of the
overall profit.
Let us now turn to the Supplier. Clearly, since decisions are decentralized, the Supplier
wants to determine his wholesale price such that his own profit is optimized, i.e., he
would use wholesale price
­
§ p W1
W1* : arg max ®(W1 c)( FD ) 1 ¨¨
© p
¯
·½
¸¸¾ .
¹¿
Unfortunately, it is not possible to derive a closed formula for the Supplier’s optimal
wholesale price S1 (W1* ) . However, it is a well-known result that if the Buyer uses the
order size Q1* (W1* ) this does not lead to an optimal SC profit, see e.g., Pasternack (1985),
Cachon (2003).
To get some more insight on the situation in the solitaire scenario, please refer to Figure
6.2. The following observations can be made.
1) As discussed, the Buyer is to weight his risk of overstocking and under stocking.
The higher the price W1 he has to pay, the higher the cost of overstocking is
( c
W1 ), the smaller the cost of under stocking ( c p W1 ). The result of
this is that the Buyer will order less at a higher wholesale price.
2) For the Supplier there are two different forces. At a higher wholesale price W1 his
margin (W1 –c) will be larger, which is positive. However, the negative side is that
at a higher price W1, the order size Q1 is lower. The Supplier is trading off these
two impacts. The result is that W1* ! c , which leads to a lower order size and
therefore a lower profit for the SC when compared to the centralized SC.
3) Only if W1
c , the overall SC profit is maximized. However, in this case all
profit goes to the Buyer, leaving the Supplier with no profit. Clearly, the Supplier
does not have any incentive to optimize the overall SC profit.
4) It is fair to assume that the Supplier and the Buyer will negotiate over what the
wholesale price W1 should be. However, no matter the outcome of the negotiation
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
is, the result will not be optimal for the SC (unless W1
c , which is not realistic
from a Supplier perspective).
Profit
Profit
π
–
B
B
T
T
S
S
0
0 C
c
W2
Figure 6.2: Profits in the base case scenario.
P
p
W
W1
Example
Throughout this chapter, the following numerical example will be used. The Buyer buys a
product from a Supplier and sells it for the fixed price p = €340. It costs the Supplier c =
€150 to produce the product. Demand for the product can be 1, 2, 3, 4, or 5 units with a
probability of 0.1, 0.2, 0.4, 0.2 and 0.1 respectively.
For these parameter values, the profits for the Buyer and the Supplier have been
calculated (see Figure 6.3). We have looked at the Supplier profit for different wholesale
price and his profit is maximum when the wholesale price is €300. Beyond this wholesale
price his profit starts to come down. With a simple wholesale price contract as is assumed
under the solitaire scenario, the Supplier will fix the wholesale price at €300. In that case
the Buyer would then decide to order 2 units as this maximizes his expected profit. The
profit for the Buyer is €46 and that for the Supplier is €300.
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136
A
B
1
Selling price
2
Cost of manufacturing
3
wholesale price
4
5 P(D)
Demand (D)
6
0.1
1
7
0.2
2
8
0.4
3
9
0.2
4
10
0.1
5
11
Expected profit (Buyer)
12
Expected profit (Supplier)
13
Expected profit (SC)
CHAPTER
C
D
E
F
6
G
340
150
300
1
40
40
40
40
40
40
150
190
Order size (Q)
2
3
-260
-560
80
-220
80
120
80
120
80
120
46
-16
300
450
346
434
4
-860
-520
-180
160
160
-214
600
386
5
-1160
-820
-480
-140
200
-480
750
270
Figure 6.3: The expected profits for the Buyer, Supplier and the SC with the wholesale
price contract
Each cell in Figure 6.3 represents the expected profit for a corresponding demand and
order quantity. It is clear from Figure 6.3 that the Buyer’s expected profit is maximum
when he orders 2 units. The SC profit in that case is €346. However, the SC profit is
maximum at €434, i.e., when the Buyer orders 3 units. Clearly, the Buyer will not be
interested in ordering that quantity as his expected profit is negative for that quantity.Ŷ
It is clear from the above analysis that in the solitaire scenario the wholesale price
contract does not have the ability to coordinate the SC. This can be intuitively explained
by observing that the entire risk associated with the demand uncertainty is taken by the
Buyer, which will discourage him from buying the SC optimal quantity. We can conclude
from our analysis that a simple wholesale price contract does not mandate risks-reward
sharing by the players. In the next sections we will review contracts in which risk sharing
is possible.
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6.3
137
Contract Mechanisms
A SC contract is an agreement between different players with respect to different trade
parameters such as pricing, order quantity commitment, periodicity of ordering, delivery
commitment and quality. For example, the agreement with respect to the pricing
parameter usually concerns:
x
How much is paid for each unit (for example this part includes wholesale price per
unit), and
x
What additional incentives are involved and how they are paid. This part includes
agreement on incentives such as quantity discount, profit sharing, revenue sharing,
credit for returned goods, et cetera.
The format of SC contracts varies across industries. Some of the commonly observed SC
contracts are the quantity discount, profit sharing, revenue sharing, and the buy-back
contract. In this section we discuss different coordination mechanisms and show that they
coordinate the SC and leads to win-win opportunities. The main objectives of the SC
contracts are:
(i)
To show that each mechanism actually is a coordinating mechanism (i.e., that the
maximum expected SC profit 3 can be achieved); and
(ii)
To show that the mechanism allows both the Supplier and the Buyer to reach a
higher expected profit level as compared to the solitaire scenario (i.e., a win-win
situation exists).
In the next section we design the revenue sharing mechanism.
6.4
Revenue sharing mechanism
In the revenue sharing mechanism (denoted by subscript 2), the transactions between the
Supplier and Buyer are governed by the Supplier charging a share of the Buyer’s
revenues ( 0 J 2 1 ) plus the wholesale price ( W2 ).
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6
The expected profits of the Supplier ( S 2 ), Buyer ( B2 ) and SC ( T2 ) in the revenue
sharing scenario are given in Table 6.2.
Situation
Supplier profit
Buyer profit
SC profit
D2 t Q2
(W2 c)Q2 J 2 p Q2
(1 J 2 ) p Q 2 W 2 Q 2
( p c)Q 2
D2 Q2
(W2 c)Q2 J 2 p D2
(1 J 2 ) p D2 W2 Q 2
pD 2 cQ 2
Table 6.2: Expected profits in the revenue sharing scenario
It follows that the expected profits are given by:
S 2 W2 , J 2 , Q2
W
2
c Q2 J 2 pQ2 pQ2 ˜ FD (Q2 ) p ˜ G D (Q2 ) (6.12)
for the Supplier;
B2 W2 , J 2 , Q2
1 J pQ
2
2
pQ2 ˜ FD (Q2 ) p ˜ G D (Q2 ) W2 Q2
(6.13)
for the Buyer; and
T2 Q2 p c Q2 pQ2 ˜ FD (Q2 ) p ˜ GD (Q2 )
(6.14)
for the SC.
The results of the revenue sharing mechanism are summarized in Theorem 6.1.
Theorem 6.1
(i)
The revenue sharing contract [W2* , J 2 ] with W2*
(1 J 2 )c will lead to a
coordinated SC.
(ii)
For any price W1 under the solitaire scenario, there is a value for J 2 and
W2 under the revenue sharing contract [W2 , J 2 ] such that both the Supplier and
the Buyer achieve higher profits than the realized profit under the solitaire
scenario.
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
Proof
(i) For any revenue sharing contract [W2 , J 2 ] the Buyer would choose Q2 such that the
expected profit B2 W2 , J 2 , Q2 is maximized. Again, the Buyer is facing a Newsvendor
problem, now the per-unit cost of overstocking is given by c W2 (item bought that
cannot be sold) and per-unit cost of under-stocking is equal to the missed profit
c
(1 J 2 ) p W2 (opportunity cost). It follows that the optimal order quantity is given
by:
Q2*
§ c
( FD ) 1 ¨¨ ©c c
·
¸¸
¹
§ (1 J 2 ) p W2 ·
¸¸ .
( FD ) 1 ¨¨
© (1 J 2 ) p ¹
From Equations (6.6) and (6.15) it is clear that if W2*
(6.15)
(1 J 2 )c then the Buyer’s optimal
order quantity is equal to the optimal SC order size in the centralized scenario. Note that
this implies that to coordinate the chain, the Supplier should sell his product at a loss, i.e.,
below marginal cost. This may be acceptable to the Supplier because he will get a share
of the Buyer’s revenue.
(1 J 2 )c, J 2 ] , the Buyer will order Q2*
Under the revenue sharing contract [W2*
Q0* ,
and the profits for the Supplier, Buyer and SC are given by S 2 (J 2 ) J 2 – ;
B2 (J 2 )
(1 J 2 ) – ; and T2
– respectively. This implies that the SC is coordinated for
all 0 J 2 1 .
(ii) The Supplier’s profit under the revenue sharing is higher than under solitaire scenario
iff:
J2 !
S1 W1
3
: (J 2 ) (6.16)
Furthermore, the Buyer’s profit under the profit sharing mechanisms is higher than the
solitaire scenario iff:
J2 Inside_proefschrift_Vijayender_06.indd 139
3 B1 W1
3
: (J 2 ) (6.17)
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140
CHAPTER
6
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. This follows immediately from:
(J 2 ) (J 2 ) =
3 B1 (W1 ) S1 (W1 )
! 0,
3
(6.18)
This completes the proof. Ŷ
Example (continued)
The performance of the revenue sharing mechanism for the numerical example is
depicted in Figure 6.4.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
A
B
Revenue sharing contract mechanism
Selling price
Cost of manufacturing
wholesale price
Revenue sharing (J)
P(D)
0.1
0.2
0.4
0.2
0.1
Expected profit(Buyer)
C
D
E
F
G
340
150
45
0.7
Demand
1
2
3
4
5
1
57
57
57
57
57
57
2
12
114
114
114
114
104
P(D)
Demand
0.1
1
0.2
2
0.4
3
0.2
4
0.1
5
Expected profit(Supplier)
Expected profit (SC)
1
133
133
133
133
133
133
190
2
28
266
266
266
266
242
346
Ordered quantity (Q)
3
4
-33
-78
69
24
171
126
171
228
171
228
130
116
Ordered quantity (Q)
3
4
-77
-182
161
56
399
294
399
532
399
532
304
270
434
386
5
-123
-21
81
183
285
81
5
-287
-49
189
427
665
189
270
Figure 6.4: The expected profits for the Buyer, Supplier and the SC with the revenue
sharing mechanism
Note that the Supplier sells the product at a wholesale price of €45 and the Buyer in turn
shares 70% of his revenues with the Supplier. It can be seen that the Buyer maximizes his
profit if he orders 3 units. The SC profit is €434 which coincides with the SC optimal
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
profit (i.e., coordination is achieved). Furthermore, it can be observed that win-win is
achieved as the profits for the Buyer and the Supplier are B2 = €130 and S2 = €304
whereas in the solitaire scenario it was B1 = €46 and S1 = €300.Ŷ
In the next section we discuss the profit sharing mechanism.
6.5
Profit sharing mechanism
In the profit sharing mechanism (denoted by subscript 3), the transactions between the
Supplier and Buyer are governed by the Supplier charging a share of the Buyer’s profits
G 3 in addition to wholesale price W3 .
The expected profits of the Supplier ( S 3 ), Buyer ( B3 ) and SC ( T3 ) with the profit
sharing mechanism are given in Table 6.3.
Situation
Supplier profit
Buyer profit
SC profit
D3 t Q3
(W3 c)Q3 G 3 ( p W3 )Q3
(1 G 3 )( p W3 )Q3
( p c)Q3
D3 Q3
(W3 c)Q3 G 3 ( pD3 W3 Q3 )
( pD3 W3 Q3 )(1 G 3 )
pD3 cQ3
Table 6.3: Expected profits in the profit sharing scenario
Expected profits for the players and the SC are given by:
S 3 W3 , G 3 , Q3
W
for the Supplier;
B3 W3 , G 3 , Q3
3
>
c Q3 G 3 p W3 Q3 pQ3 ˜ FD Q3 p ˜ G D (Q3 )
1 G > p W Q
3
3
3
pQ3 ˜ FD Q3 p ˜ G D (Q3 )
@
@
(6.19)
(6.20)
for the Buyer; and
p c Q
T3 Q3
3
pQ3 ˜ FD Q3 p ˜ GD (Q3 )
(6.21)
for the SC.
The results of the profit sharing mechanism are summarized in Theorem 6.2.
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CHAPTER
6
Theorem 6.2
(i)
The profit sharing mechanism [W3* , G 3 ] with W3*
c will lead to a coordinated SC
for all G 3 .
(ii)
For any price W1 under the solitaire scenario, there is a value for G 3 and
W3 under the profit sharing scenario [W3* , G 3 ] such that both the Supplier and the
Buyer achieve higher profits than the realized profits under the solitaire scenario.
Proof:
(i) For any profit sharing contract [W3 , G 3 ] the Buyer would choose the order size such
that the expected profit B3 W3 , G 3 , Q3 is maximized. Since the profit for the Buyer is a
fraction (1 G 3 ) of the Buyer’s profit under the solitaire scenario, it is easy to see that the
Buyer’s optimal order quantity is given by:
Q3* (W3 )
1 § p W3
FD ¨¨
© p
·
¸¸.
¹
(6.22)
Note that this expression does not depend on G 3 . Also note that if the wholesale price
W3 is set equal to the cost price c , the Buyer’s optimal order size is equal to the optimal
SC order size in the centralized scenario. At first glance it might not seem to be
interesting to the Supplier to set the wholesale price equal to the cost. However, unlike in
the solitaire scenario, setting the wholesale price equal to the cost price can be acceptable
to the Supplier because he will still get a share of the Buyer’s profit.
Assuming that W3*
c , it follows that the Buyer uses his optimal order quantity Q3*
Q0* ,
and, consequently, the profits for the Supplier, Buyer and SC are given by
S 3 (G 3 ) G 3 – ; B3 (G 3 ) (1 G 3 ) – and T3
– respectively.
(ii) The proof of win-win for the profit sharing mechanism follows on the same lines as
that of the revenue sharing mechanism, see Theorem 6.1 (ii) and is therefore omitted
here.Ŷ
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
Example (continued)
Figure 6.5 presents the results of the numerical example for the profit sharing mechanism.
A
B
1 Profit sharing contract mechanism
2
Selling price
3
Cost of manufacturing
4
Wholesale price
Profit sharing (G)
5
6
7
P(D)
Demand
8
0.1
1
9
0.2
2
10
0.4
3
11
0.2
4
12
0.1
5
13
Expected profit (Buyer)
14
15
P(D)
Demand
16
0.1
1
17
0.2
2
18
0.4
3
19
0.2
4
20
0.1
5
21
Expected profit (Supplier)
22
Expected profit(SC)
C
D
E
F
G
340
150
150
0.7
1
57
57
57
57
57
57
2
12
114
114
114
114
104
1
133
133
133
133
133
133
190
2
28
266
266
266
266
242
346
Order quantity (Q)
3
-33
69
171
171
171
130
Order quantity (Q)
3
-77
161
399
399
399
304
434
4
-78
24
126
228
228
116
5
-123
-21
81
183
285
81
4
-182
56
294
532
532
270
386
5
-287
-49
189
427
665
189
270
Figure 6.5: The expected profits for the Buyer, Supplier and the SC with the profit
sharing mechanism
From Figure 6.5 the Supplier fixes the wholesale price at €150 and the Buyer shares 70%
of his profits with the Supplier. It is clear from row 13 that the Buyer’s expected profit is
maximized when Q3 = 3 units. The resulting SC profit is €434 which is equal to the
maximum SC profit (i.e., the SC is coordinated). Furthermore, it can be observed that
win-win is achieved as the profits for the Buyer and the Supplier are B3 = €130 and S3 =
€304 whereas in the solitaire scenario it was B1 = €46 and S1 = €300.Ŷ
In the next section we discuss the License fee mechanism.
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144
6.6
CHAPTER
6
License fee mechanism
In the license fee mechanism (denoted by subscript 4) the transactions between the
Supplier and Buyer are governed by the Supplier charging a fixed license fee L4 in
addition to the wholesale price W4 .
The expected profits of the Supplier ( S 4 ), Buyer ( B4 ) and SC ( T4 ) in the license fee
scenario are given in Table 6.4.
Situation
Supplier profit
Buyer profit
SC profit
D4 t Q4
(W4 c)Q4 L4
( p W4 )Q4 L4
( p c)Q 4
D4 d Q4
(W4 c)Q4 L4
pD4 W4 Q4 L4
pD 4 cQ4
Table 6.4: Expected profits with the license fee scenario
The expected profits are given by:
S 4 W4 , L4 , Q4
(W4 c)Q4 L4
(6.23)
for the Supplier;
B4 W4 , L4 , Q4 p W Q
4
4
pQ4 ˜ FD Q4 p ˜ G D (Q4 ) L4
(6. 24)
for the Buyer; and
p c Q
T4 Q4
4
pQ4 ˜ FD Q4 p ˜ GD (Q4 )
(6.25)
for the SC.
The results of the license fee mechanism are summarized in Theorem 6.3.
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
ii)
For any price W1 under the solitaire scenario, there are values of L4 under the
License fee mechanism [W4* , L4 ] such that both the Supplier and the Buyer achieve
higher profits than the realized profit under the solitaire scenario,
Proof
(i) For any wholesales price W4 and license fee L4 , the Buyer would choose the order
size such that his expected profit B4 W4 , L4 , Q4 is maximized. The optimal order
quantity is therefore given by:
Q4*
1 § p W4
FD ¨¨
© p
·
¸¸.
¹
(6.26)
Clearly, the Buyer’s order size under the two part tariff mechanism will lead to the
optimal order size as under the centralized scenario if and only if W4*
wholesale price is equal to marginal the cost. If W4*
c then T4 Q4*
c , i.e., the
– , i.e., the SC is
coordinated. Note that such a wholesale price is acceptable to the Supplier because he
will get the license fee L4 .
(ii) Assuming W4*
B4
c , the resulting profits for the Supplier and the Buyer are S 4
L4 and
– L4 respectively. The Supplier’s profit under the license fee mechanism is higher
than under solitaire scenario if:
L4 ! S1 W1
(6.27)
: L4 .
Furthermore, the Buyer’s profit under the license fee mechanisms should be higher than
the solitaire scenario profit, i.e.,
L4 3 B1 W1
: L4
(6.28)
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. i.e.,
L4 L4
Inside_proefschrift_Vijayender_06.indd 145
3 B1 (W1 ) S1 (W1 ) ! 0
(6.29)
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146
CHAPTER
6
It follows immediately that the right hand side of Equation (6.29) is always nonnegative
as the profit in the centralized scenario will be greater than the solitaire scenario.Ŷ
Example (continued)
For the numerical example the performance of the license fee mechanism can be obtained
as shown in Figure 6.6.
A
B
1 License fee contract mechanism
2
Selling price
3
Cost of manufacturing
4
wholesale price
5
License-Fee
6
7
P(D)
Demand
8
0.1
1
9
0.2
2
10
0.4
3
11
0.2
4
12
0.1
5
13
Expected profit (Buyer)
14
Expected profit(Supplier)
15
Expected profit (SC)
C
D
E
F
G
340
150
150
350
1
190
190
190
190
190
-160
350
190
2
40
380
380
380
380
-4
350
346
Ordered quantity (Q)
3
4
-110
-260
230
80
570
420
570
760
570
760
84
36
350
350
434
386
5
-410
-70
270
610
950
-80
350
270
Figure 6.6: The expected profits for the Buyer, Supplier and the SC for the license fee
mechanism
In Figure 6.6 the wholesale price is €150 and license fee is €350. The Buyer orders 3
units. At this ordered quantity the SC profit is equal to €434 (i.e., the SC is coordinated).
Furthermore, B4 = €80 and S4 = €350 whereas B1 = €46 and S1 = €300. It follows that
win-win is achieved.Ŷ
In the next section we discuss the buy-back contract mechanism.
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6.7
147
Buy-back contracts
In the buy-back contract mechanism (denoted by subscript 5) the transactions between
the Supplier and Buyer are primarily governed by the Supplier charging a wholesale price
( W5 ). However, the Buyer can return a certain percentage ( 0 d U 5 d 1 ) of the left-over
items at the end of the selling season at a certain return price W 5 (with 0 d W 5 d W5 ). If
W5
W5 , the contract is said to be full refund. If U 5
1 , the contract is said to be full
return, in which case the Buyer can return all the unsold items at the end of the season. If
U 5 1 , the contract is said to be partial return as the Buyer can only return a limited
number of the unsold items to the Supplier.
Buy-back contracts (also called return policies) are common for instance in the
distribution of books, magazines, newspapers, recorded music, computer hardware and
software, greeting cards and pharmaceuticals. For example, college bookstores return
about 40% of all new textbooks (see Padmanabhan & Png (1997)). According to the
Association of American Publishers, 35% worth of all hard covers shipped to buyers’ in
1996 were returned to publishers (see Bruce (1997)). The rationale behind the buy-back
contract is that allowing the Buyer to return unsold units reduces his risk of overstocking
and thus will motivate him to order more. This in turn increases availability to the final
consumer and therefore positively influences overall sales (hence profit).
In the buy-back contract, the three situations are possible, see Table 6.5.
Situation
Supplier profit
Buyer profit
SC profit
D5 t Q 5
(W5 c)Q5
( p W5 )Q5
( p c)Q5
(1 U 5 )Q5 d D5 d Q5
(W5 c)Q5 W 5 (Q5 D5 )
pD5 W5 Q5 W 5 (Q5 D5 )
pD5 cQ5
D5 d (1 U 5 )Q5
(W5 c)Q5 W 5 U 5 Q5
pD5 W5 Q5 W 5 U5 Q5
pD5 cQ5
Table 6.5: Profits under the buy-back scenario.
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6
Careful analysis shows that the expected profits are given by:
S 5 U 5 ,W 5 ,W5 , Q5
W
5
c Q5 W 5 ˜ Q5 ˜ FD Q5 W 5 ˜ G D Q5 (1 U 5 )W 5 ˜ FD ((1 U 5 )Q5 ) W 5 ˜ G D ((1 U 5 )Q5 )
(6.30)
for the Supplier;
B5 U 5 ,W 5 ,W5 , Q5
p W Q
5
5
(W 5 p)Q5 ˜ FD Q5 ( p W 5 )G D Q5 (1 U 5 )W 5 ˜ Q5 ˜ FD ((1 U 5 )Q5 ) W 5 ˜ G D ((1 U 5 )Q5 )
(6.31)
for the Buyer; and
p c Q
T5 Q5
5
p.Q5 ˜ FD Q5 p ˜ GD (Q5 )
(6.32)
for the SC.
The performance of the buy-back contract is summarized in Theorem 6.4.
Theorem 6.4:
(i)
The buy-back contact [W5 ;W 5 ; U 5 ] with FD (1 U 5 )Q5* cW
§
¨ (c W5 ) W 5 5
p
¨
¨
W 5 (1 U 5 )
¨
©
·
¸
¸
¸
¸
¹
coordinates the SC for any given W 5 and U5 .
(ii)
For each price 0 U 5 d 1 , there exists an infinite number of combinations of W5
and W 5 in the returns payment scenario such that both the Supplier and the Buyer
have higher expected profits with [W5 ;W 5 (W5 ); U 5 ] than the profits under the
solitaire scenario with W1 ! c .
Proof
(i) For any wholesale price W5 and payback price W 5 , the Buyer prefers to choose Q5
such that the expected profit B5 U 5 ,W 5 ,W5 , Q5 in Equation (6.31) is maximized.
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COORDINATING PRICING AND REPLENISHMENT DECISIONS IN A SC WITH UNCERTAIN DEMAND
Let Q5* satisfy:
dB5 *
(Q5 )
dQ
( p W5 ) (W 5 p) FD Q5* ( U 5 1)W 5 FD ((1 U 5 )Q5* )
0.
§ pc·
¸¸ . The Buyer will
From the centralized scenario analysis we know that FD (Q0* ) ¨¨
© p ¹
Q5 )
31)
choose his optimal quantity the same as in the centralized scenario when Q5*
Q0* , i.e.,
when:
§ pc·
¸¸ ( U 5 1)W 5 FD ((1 U 5 )Q5 ) =0
( p W5 ) (W 5 p )¨¨
© p ¹
which is equivalent to:
(c W5 ) W 5 FD ((1 U 5 )Q5* )
cW 5
p
W 5 (1 U 5 )
.
(6.33)
using Equation (6.33), the profits can be obtained as:
B5 Q5*
( p W 5 )G D Q5* W 5 ˜ G D ((1 U 5 )Q5* )
(6.34)
for the Buyer;
S 5 Q5*
W 5*G D Q5* W 5 ˜ G D ((1 U 5 )Q5* )
(6.35)
for the Supplier; and
T5 Q5*
p ˜ G D (Q5* )
p ˜ G D Q0*
–
(6.36)
for the SC.
From the Equation (6.36) it is clear that the SC profit is same as that in the centralized
scenario (i.e., the SC is coordinated).
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150
CHAPTER
(ii) Assuming that FD (1 U 5 )Q5*
cW
§
¨ (c W5 ) W 5 5
p
¨
¨
W 5 (1 U 5 )
¨
©
6
·
¸
¸ and that the Buyer uses his
¸
¸
¹
optimal order quantity Q5* , the profits for the Supplier and the Buyer can be obtained from
Equations (6.35) and (6.34) as:
W 5 ¨¨
·
§–
GD ((1 U5 )Q5* ¸¸ ; and
¹
© p
(6.37)
·
§–
– W 5 ¨¨ GD ((1 U5 )Q5* ¸¸ .
¹
© p
(6.38)
S5 Q5*
B5 Q5*
It follows that the Supplier’s profit with the buy-back contract is higher than under
solitaire scenario iff:
W5 !
S1 (W1 )
§–
¨¨ GD (1 U5 )Q5*
© p
·¸¸
: W 5 .
(6.39)
¹
Furthermore, the Buyer’s profit with the Buy-back contract is higher than the solitaire
scenario profit, iff:
W5 – B1 (W1 )
§–
¨¨ GD (1 U5 )Q5*
© p
·
¸¸
¹
=: W 5
(6.40)
In order to complete the proof, it remains to be shown that the upper bound is always
greater than the lower bound. This immediately follows from:
W 5 W 5 =
3 B1 (W1 ) S1 (W1 )
! 0.
§–
*·
¨¨ GD ((1 U5 )Q5 ¸¸
¹
© p
(6.41)
In addition to the above analysis it is worthwhile to consider two special cases, namely
full returns (U5 = 1) and no returns (U5 = 0). In the case of full returns, it follows
that G D ((1 U 5 )Q5*
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0 , so that B5
§ p W 5 ·
¸¸ – ; S 5
¨¨
© p ¹
W5
p
– ; and
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W 5 W 5
p
3 B1 (W1 ) S1 (W1 ) ! 0 .
3
If there are no returns then G D (1 U 5 )Q5* 3
, so that B5
p
– ; S5
0 which
corresponds to the solitaire scenario (so that win-win is not possible). This completes the
proof. Ŷ
Example (continued)
The results of the numerical example with the buy-back contract are presented in the
Figure 6.7.
A
B
1 Buy-back or Return policies
2
Selling price
3
Cost of manufacturing
4
Wholesale price
5
Refund value
6
Quantity returns allowed
7
8
P(D)
Demand (D)
9
0.1
1
10
0.2
2
11
0.4
3
12
0.2
4
13
0.1
5
14
Expected profit (Buyer)
15
16
P(D)
Demand(D)
17
0.1
1
18
0.2
2
19
0.4
3
20
0.2
4
21
0.1
5
22
Expected profit (Supplier)
23
Expected profit (SC)
C
D
E
F
G
340
150
300
290
0.4
1
40
40
40
40
40
40
1
150
150
150
150
150
150
190
Ordered quantity (Q)
3
4
20
-280
70
60
120
110
120
160
120
160
100
76
Ordered quantity (Q)
2
3
4
10
-130
20
300
160
20
300
450
310
300
450
600
300
450
600
271
334
310
346
434
386
2
30
80
80
80
80
75
5
-580
-240
100
150
200
-16
5
170
170
170
460
750
286
270
Figure 6.7: Expected profits for the Buyer, Supplier and the SC for the buy-back policy
Figure 6.7 represents the buy-back contract with W 5
290 and U 5
0.4 , which implies
that the Supplier will accept 40% of the left-over items at a refund value of €290. It is
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6
clear from row 13 that the Buyer’s expected profit is maximized when Q5 = 3. The
resulting SC profit is €434 which is equal to the maximum SC profit (i.e., the SC is
coordinated). Furthermore, it can be observed that win-win is achieved as the profit for
the Buyer and the Supplier are B5 = €100 and S5 = €334 whereas in the solitaire scenario
it was B1 = €46 and S1 = €300.Ŷ
In the next section we conclude the study and provide some interesting managerial
insights.
6.8
Conclusions
It has been shown that all the coordination mechanisms considered in this chapter
coordinate the channel and lead to win-win situations. From a mathematical point of view
all these mechanisms may seem identical, or at least closely related. However, from an
implementation point of view there are some significant differences between the several
mechanisms discussed in this paper. In this section, we will shortly review the
commonalties and difference between the discussed mechanisms.
A first important observation is that all the mechanisms require a certain level of
information exchange. For instance, in the profit sharing mechanism, the Buyer is to
reveal his profit to the Supplier simply because part of the profit will be transferred to the
Supplier. For the license fee mechanism, giving such insight into his profitability is not
necessary for the Buyer because all that is transferred is a predetermined fixed lump sum.
Although not directly visible from our models, this notion implies that the license fee and
buy-back mechanisms are probably easier to implement than the profit sharing and
revenue sharing mechanism.
A second observation is that in our model we used the criterion of maximizing expected
profits. It is to be noted that in the solitaire scenario the Supplier will have a guaranteed
(risk-free) profit. In all the theorems it was shown that the Supplier will win from
applying the coordinating mechanisms. However, “winning” here only implies a higher
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153
expected profit. A risk-avoiding Supplier might not be satisfied by merely a higher
expected profit; depending on his level of risk- averseness, the Supplier might want to be
more than compensated for taking risk in the entire operation. From the Supplier’s point
of view it would even be better to simply have a higher risk-free profit. It is easy to see
that the license fee mechanism does offer this feature, whereas the profit sharing and
revenue sharing necessarily imply that the Supplier does take risk. In Webster & Weng
(2000) it has been shown that also in the buy-back mechanism for certain parametersettings; a risk-free larger profit for the Supplier can be achieved.
There are many ways in which this work can be expanded. One possible addition could
be to add the possibility of the Buyer setting the final selling price. Another interesting
model would follow from adding several competing Suppliers and Buyers. Also, it might
be of interest to study the possibility of reordering once or twice and see the impact of a
Supplier able to quickly respond to demand. All these extension might lead to more
insights on how SC collaboration can be profitable to all parties involved without losing
too much of one’s own identity.
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Part 2: Contract Mechanisms for Coordinating
Promotional Decisions in a Supply Chain
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157
Chapter 7
Using Promotion Mechanisms to Coordinate Decisions in a Supply
Chain with Price Sensitive Demand 7
Chapter Synopsis
In this chapter, we design different mechanisms related to promotions for coordinating
decisions in a Supply Chain (SC) and test their ability to provide a win-win solution for
all the players. A SC setting in which the end-consumer demand is price sensitive and
deterministic is considered. It is shown that direct rebates (mail-in-rebate) and trade
promotion (supplier rebate) do not provide coordination and win-win opportunities
simultaneously. We design a new mechanism called combined rebate mechanism and
show that it can provide both SC coordination and win-win opportunities.
7.1
Introduction
Sales promotion consists of a diverse collection of incentive tools, designed to stimulate
demand for particular products or services. The Supplier can choose to provide a price
reduction directly to the end customer upon the purchase of the merchandise and
redemption of rebate coupons immediately or at a later stage (see e.g., Anderson & Song,
(2004); Arcelus & Srinivasan, (2003); McGuiness, (2003); Nevo & Wolfram, (2002)). In
practice, companies like Nikon and Sharp, to name a few, provide discount directly to the
end-consumer (See Simchi Levi et al. (2003), p.251). Such discount mechanisms are
referred to as mail-in-rebate mechanisms as the consumer can get back the discount
amount after mailing the rebate coupon. The Supplier could also decide to provide a
rebate to the Buyer, which is known as Supplier rebate, also called trade promotions. The
7
This chapter is the modified and updated version of the paper presented at the 13th EurOMA conference in
Glasgow [Reference: Nalla, V. R, J.A.A van der Veen, and V. Venugopal (2006b)]
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Buyer can also choose to provide the rebate to the end-consumer in which case those
mechanisms are called the consumer rebate mechanisms. Figure 7.1 gives a
representation of the different rebate mechanisms.
Supplier
Supplier
rebate
Supplier
rebate
Supplier
Buyer
Buyer
Direct rebate
- Direct
rebate
End consumer
End consumer
Consumer rebate
Consumer rebate
Figure 7.1: Supply chain with different possible rebates
In addition to the promotion mechanisms discussed above, it is also possible for the
Supplier to offer a rebate to the Buyer after ensuring that the Buyer has passed on the
intended rebate to the end-consumer. In this study, we design one such mechanism which
combines the Supplier and consumer rebates. As the rebate is provided by both the
players simultaneously, we call it the combined rebate mechanism.
7.2
Basic model and Analysis
Consider a two-echelon SC with a Buyer and a Supplier. The Supplier sells a product
with a short life cycle (e.g., a fashion product) to the Buyer, who resells the product to the
consumers, see Figure 7.2.
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Supplier
Buyer
159
C
O
N
S
U
M
E
R
S
Figure 7.2: A simple SC
The setting is similar to the one considered in Chapter 3; however, our focus here is to
coordinate the promotion decisions in a SC. As in Chapter 3, we assume that the final
customer demand D for the product depends linearly on the price P set by the Buyer:
D( P) D EP ,
(7.1)
where 0 d c P d D E and c d W d P .
The profit for the Supplier, Buyer and the SC can be obtained as:
S : W c Q ;
B:
(7.2)
P W Q ; and
(7.3)
P c Q
(7.4)
T: SB
respectively.
In the solitaire scenario (denoted by subscript 1), the Supplier will set a wholesale price
W which will optimize his profits, and the Buyer will choose a final selling price P to
optimize his profits. As demonstrated in Chapter 3, the wholesale price and final selling
price are given by:
W1* :
D Ec
;
2E
(7.5)
and,
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CHAPTER
P1* :
3D E c
.
4E
–:
D Ec 2 ,
7
(7.6)
Defining,
(7.7)
4E
it follows that the profits for the Buyer, Supplier and the SC under the solitaire scenario
can be obtained as: B1
–
; S1
4
–
and T1
2
3–
. Recall from Chapter 3 that the
4
optimal profit in the centralized scenario (i.e., if the Buyer and Supplier would operate as
a single organization) is equal to – .
Example
Throughout this chapter, we will use the following numerical example. Let
D( P) 100 2 P , i.e., D
100 and E
2 . Furthermore, let c
30 . The final selling
price and the profits for Buyer, Supplier and the SC under the centralized and the solitaire
scenario are provided in Table 7.1. Ŷ
No. Scenario
W
P
Q
B
S
T
0
Centralized
n/a
40
20
n/a
n/a
200
1
Solitaire
40
45
10
50
100
150
Table 7.1: Centralized vs. solitaire scenario results (Numerical example)
To overcome the observed sub-optimization in the solitaire scenario (the so-called double
marginalization), in this chapter we will review contract mechanisms that are related to
promotions. First we analyze the performance of the mail-in-rebate with two different
rebate values: one which is optimal for the Supplier and another which is optimal for the
SC. The performance of the simple wholesale price discount (Supplier rebate or trade
promotion) is compared with the performance of the mail-in-rebate mechanism. Later, a
combined rebate mechanism is designed and the conditions for coordination and win-win
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161
opportunities are obtained. The performance of the combined rebate mechanism is
compared with that of the mail-in-rebate. Finally, we conclude the study.
7.3 Mail-in-Rebate
With the mail-in-rebate mechanism, the Supplier will credit the end-consumer with an
amount equal to the value of the rebate coupon. All that the end-consumer has to do, after
purchasing the product from the Buyer, is to mail the rebate coupon back to the Supplier.
The Supplier will reimburse the consumer with the amount of the rebate coupon. Note
that in this way, the Supplier directly influences end-consumer demand and thus
motivates the Buyer to increase his order quantity. By introducing the rebate, the
effective price paid by the end-consumer is reduced, and hence the Buyer faces a higher
demand. Since we assume information symmetry between the Buyer and the Supplier, the
Buyer is fully aware of the rebate provided to the end-consumer, which will enable him
to adjust his order quantity appropriately, see also Simchi Levi et al. (2003, p. 251). The
following sequence of events takes place with the mail-in-rebate mechanism:
1) The Supplier introduces a new fashionable product and communicates the wholesale
price to the Buyer;
2) Based on the price dependent function, the Buyer will optimize his profit and
announce (or prints a catalogue with) the final selling price. This will prevent the
Buyer from changing the price of the product at a later stage of the selling season;
3) The Supplier then sees a potential to make a greater profit by providing a rebate
directly to the end-consumers and announces a rebate value;
4) Finally, the Buyer will decide the order quantity, after knowing the rebate value
provided to the end-consumers.
Under the mail-in-rebate mechanism (denoted by subscript 2), the Supplier fixes the
wholesale price and the Buyer will fix the final selling price the same as in the solitaire
scenario, i.e.,
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CHAPTER
W2*
P2*
W1*
P1*
7
D Ec
; and
2E
(7.8)
3D Ec
.
4E
(7.9)
After the Buyer determined his selling price, the Supplier determines the rebate that he
would be willing to provide to the end-consumers. The actual price paid by the endconsumer when the Supplier provides a rebate R2 after the Buyer makes a decision on
his final selling price can be obtained as:
P2
P1* R2
3D Ec
R2 .
4E
(7.10)
Since the Buyer makes a decision on his order quantity after the Supplier decides on the
rebate he will provide to the end-consumers, the profit for the players and the SC with the
mail-in-rebate mechanisms can be obtained as:
S2
(W 2 c R 2 ) D E ( P1* R 2 ) ;
(7.11)
B2
( P1* W 2 ) D E ( P1* R 2 ) ; and
(7.12)
T2
( P1* c R 2 ) D E ( P1* R 2 ) .
(7.13)
The results of the mail-in-rebate mechanism are summarized in the following theorem.
Theorem 7.1
(i)
The rebate value which is optimal for the Supplier does not coordinate the SC but
leads to a win-win situation.
(ii)
For the rebate value which is optimal for the SC, the Supplier’s profit is the same
as that of the solitaire scenario. The entire additional profit is taken up by the
Buyer.
Proof
(i) A rebate value which will optimize the Supplier’s profit (denoted by subscript 2) can
be obtained by determining the value of R2 which will optimize the Supplier’s profit
function as given in Equation (7.11).
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163
By using the first order derivative with respect to the Supplier’s profit function, it can be
seen that the rebate value which will maximize his profit is given by:
R2*
1
(D Ec) .
8E
(7.14)
When the Supplier provides a rebate as given in Equation (7.14), the end-consumer
demand, hence the Buyer’s order quantity can be obtained as:
Q2*
3
8
(D Ec) .
(7.15)
Recall that the order quantity in the solitaire scenario is Q1*
order quantity is Q0*
1
2
1
4
(D Ec) . The SC optimal
(D Ec) . It follows from Equation (7.15) that in that sense the
“gap” is closed by 50% when the Supplier offers a mail-in-rebate which is optimal for
him. Furthermore, when the Supplier decides to provide a rebate which is optimal for
him, the profits for the Buyer, Supplier, and the SC can be obtained as:
B2
S2
T2
6
(D Ec) 2
64E
9
(D Ec) 2
64 E
15
(D Ec) 2
64E
33
;
8
(7.16)
93
; and
16
(7.17)
153
16
(7.18)
respectively. Comparing the profits of the players and the SC with the mail-in-rebate to
those profits obtained in solitaire scenario gives the following results:
B2 B1
3
;
8
(7.19)
S 2 S1
3
; and
16
(7.20)
T2 T1
33
.
16
(7.21)
The positive values in Equations (7.19) and (7.20) show that win-win opportunities are
obtained. Furthermore, since T2 3 it is clear that the supply chain is not coordinated.
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7
(ii) Let R3 be the rebate value which will optimize the SC profit (where the subscript 3
refers to the scenario where the SC optimal mail-in-rebate value is used). Updating the
notation within Equation (7.13), the profit function for the SC with rebate R3 can be
obtained as:
T3
( P1* c R3 ) D E ( P1* R3 ) .
(7.22)
The first order condition provides the following optimal rebate value:
R3*
1
D Ec .
4E
(7.23)
The optimal rebate in Equation (7.23) allocates the following profits for the Buyer,
Supplier, and the SC:
B3
(D Ec) 2
8E
3
;
2
(7.24)
S3
(D E c) 2
8E
3
; and
2
(7.25)
T3
(D Ec) 2
4E
3.
(7.26)
It can be concluded that at the rebate value which is optimal for the SC, the Supplier’s
profit is the same as that in the solitaire scenario, that all the additional profit from the
rebate goes to the Buyer and the SC profit is optimized, i.e., the SC is coordinated.Ŷ
Figure 7.3 summarizes the resulting profits within the solitaire scenario (R=0), the
supplier’s optimal rebate value R2* and the SC optimal rebate value R3* .
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USING PROMOTION MECHANISMS TO COORDINATE DECISIONS IN A SUPPLY CHAIN WITH PRICE SENSITIVE DEMAND
π
ʌT
3π/4
T
Profits
3ʌ/4
S
Profits
π /2
ʌ/2
ʌ/4
π /4
B
S
B
0
1
2
R 2*
R 2*
3
4
5
R ebate v alue
R 3*
R 3*
6
7
Rebate value
Figure 7.3: Profit for the Supplier (S), Buyer (B) and the supply chain (T) with the mailin-rebate mechanism
Example (continued)
The results for the mail-in-rebate with an optimal rebate value as determined by the
Supplier (scenario 2) and optimal rebate value as determined by the SC (scenario 3) are
provided in the Table 7.2.
No. Scenario
R/d
W
P
Q
B
S
T
0
Centralized
n/a
n/a
40
20
n/a
n/a
200
1
Solitaire
n/a
40
45
10
50
100
150
2
Mail-in-rebate
2.5
40
45-2.5
15
75
112.5
187.5
5
40
45-5
20
100
100
200
Supplier opt
3
Mail-in-rebate
SC-optimal
Table 7.2: Mail-in-rebate mechanism results (Numerical example)
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The value of P given in the Table 7.2 is the price as experienced by the consumers. It can
be observed that indeed scenario 2 leads to win-win when compared to the solitaire
scenario (scenario 1) but not to a coordinated SC. Furthermore, scenario 3 leads to a
coordinated SC but does not increase the profit of the Supplier.Ŷ
In the next section, we design the wholesale price discount (Supplier rebate) that the
Supplier provides to the Buyer, and compare its performance with that of the mail-inrebate mechanism.
7.4
Wholesale price discount analysis
Instead of providing the rebate to the end-consumer, as discussed in the previous section,
the Supplier can also choose to provide a wholesale price discount to the Buyer. The
following sequence of events takes place under this so-called wholesale price discount
mechanism:
1) The Supplier introduces a new fashionable product, and communicates the
wholesale price per unit and the discount that he is going to provide to the Buyer;
2) Based on the price dependent function, the Buyer will optimize his profit and
announces the final selling price;
3) The Buyer’s selling price determines the final demand and the Buyer will place an
order for the appropriate number of units.
It is immediately clear that within the wholesale price discount scenario, both the
wholesale price and the discount are targeted at the Buyer and that together these
parameters determine the decision of the Supplier. In other words, as determined at the
discussion of the solitaire scenario, the wholesale price W4 and discount d4 (where the
subscript 4 refers to the wholesale price discount scenario) are optimal to the Supplier as
long as
W4
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W1* d 4 .
(7.27)
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However, since it is our objective to compare the performance various types of promotion
mechanisms, we are not looking for the optimal values, but will take another approach.
R2* , i.e., a discount value which is equal to the
We will consider a discount value d 4
optimal mail-in-rebate value chosen by the Supplier in Scenario 2 and compare the
performance of the wholesale price mechanism to the mail-in-rebate mechanism.
Following this logic, it follows from Equations (7.5) and (7.14) that:
W4* W1* d 4
1
8E
3D 5Ec .
(7.28)
When the Supplier sets the wholesale price as given in Equation (7.28), the Buyer sets the
following selling price:
P4*
1
11D 5Ec .
16E
The resulting profits for the Supplier, Buyer and the SC are: B4
T4
55
64
(7.29)
25
16
–
; S4
4
15
16
–
; and
2
–.
Comparison of the profits made by the players with the wholesale price discount
mechanism and the solitaire scenario gives the following:
B4 B1
25
16
– –
4 4
9
64
S 4 S1
30
16
– –
4 2
642 – 0 ; and
(7.31)
– ! 0.
(7.32)
T4 T1
55
16
– 3–
4
4
– ! 0;
7
64
(7.30)
It can be concluded that the Buyer and the SC obtain additional profit when compared to
the Solitaire scenario. However, the Supplier receives a lower profit than in the solitaire
scenario. Furthermore, since
T4 T0
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55
16
–
3
4
649 3 0 ,
(7.33)
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CHAPTER
7
we can conclude that the optimal SC is not obtained. Summarizing, the wholesale price
discount mechanism neither coordinate the SC, nor does it provide win-win.
Example (continued)
Table 7.3 shows how the wholesale price scenario compares to the centralized, the
solitaire and the mail-in-rebate mechanisms for the numerical example.Ŷ
No. Scenario
R/d
W
P
Q
B
S
T
0
Centralized
n/a
n/a
40
20
n/a
n/a
200
1
Solitaire
n/a
40
45
10
50
100
150
2
Mail-in-rebate
2.5
40
45-2.5
15
75
112.5
187.5
2.5
37.5
43.75
12.5
125
67.5
187.5
Supplier opt
4
Wholesale price
discount
Table 7.3: Wholesale price discount results (Numerical example)
In the following subsection a detailed analysis is provided on how the wholesale price
discount mechanism compares to the mail-in-rebate mechanism.
7.4.1
Mail-in-rebate Vs Wholesale price discount
In this part of the analysis, we compare the profits of the players and the SC with the
wholesale price discount to the profits realized through the mail-in-rebate mechanism.
The difference in the profit for the Buyer can be obtained as:
B4 B2
25
16
– 24 –
4 16 4
1
16
–
! 0.
4
(7.34)
The positive value for the Equation (6.34) shows that the Buyer obtains an additional
profit with the wholesale price discount when compared to the mail-in-rebate mechanism.
Figure 7.4 indicates the profit for the Buyer for the two mechanisms (using the values
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USING PROMOTION MECHANISMS TO COORDINATE DECISIONS IN A SUPPLY CHAIN WITH PRICE SENSITIVE DEMAND
from the numerical example) for various values of the rebate ( R2 ) and discount (d4)
respectively.
Ʌ
π
3π/4
Profit
Profit
3Ʌ/4
π /2
Ʌ/4
π /4
Ʌ/2
0
2
4
6
8
10
Mail-in-Rebate / Wholesale Price Discount
Mail-in-Rebate/Wholesale price discount
Mail-in-Rebate
wholesale price discount
Mail-in-Rebate
Wholesale price discount
Figure 7.4: Comparing the performance of the Buyer with the mail-in-rebate and
wholesale price discount mechanisms.
It is clear from Figure 7.4 that for any given wholesale price discount that is the same as
the mail-in-rebate value, the Buyer makes a greater profit with the wholesale price
discount than with the mail-in-rebate mechanism.
The difference in profits for the Supplier can be obtained as:
S4 S2
30
16
– 36 –
4 16 4
166
–
0.
4
(7.35)
The negative value in the Equation (7.35) indicates that for any given rebate value which
is the same as the wholesale price discount, the Supplier’s profit is always higher with the
mail-in-rebate mechanism. The reason for this is that, since within the mail-in-rebate
mechanism the total discount is passed on directly to the end-consumer, the increase in
the consumer demand with the mail-in-rebate mechanism is higher than the increase with
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the wholesale price discount mechanism. Figure 7.5 indicates the profit of the Supplier
with the two mechanisms (using the values as in the numerical example) for various
values of the rebate ( R2 ) and discount (d4) respectively.
Ʌ/2
Profit
Profit
π /2
0
2
4
6
8
10
Mail-in-rebate/Wholesale price discount
Mail-in-Rebate/Wholesale price discount
Mail-in-Rebate
w holesale price discount
Mail-in-Rebate
Wholesale price discount
Figure 7.5: Comparing the performance of the Supplier with mail-in-rebate and
wholesale price discount mechanisms
As can be seen from Figure 7.5, the Supplier earns a greater profit with the mail-in-rebate
as compared to the wholesale price discount.
The additional total profit for the SC is:
T4 T2
55
16
– 60 –
4 16 4
165
–
0.
4
(7.36)
The negative value in Equation (7.36) indicates that the supply chain profit is higher with
the mail-in-rebate mechanism. The reason for this is that the increase in profit due to
additional demand is higher than the profit decrease due to the reduction in the effective
final selling price. Figure 7.6 shows the profit for the SC with the two mechanisms (with
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171
values from the numerical example) for various values of the rebate ( R2 ) and discount
(d4) respectively.
Ʌ
π
Profit
3Ʌ/4
3π/4
Profit
Ʌ/2
π /2
Ʌ/4
π /4
0
2
4
6
8
10
Mail-in-Rebate/wholesale price discount
Mail-in-Rebate
wholesale price discount
Mail-in-Rebate/Wholesale price discount
Mail-in-Rebate
Wholesale price discount
Figure 7.6: Comparing the performance of the supply chain under the mail-in-rebate and
wholesale price discount mechanism
Figure 7.6 shows that from a SC perspective, the mail-in-rebate performs better than the
wholesale price discount to a certain threshold value (which is equal to the optimal mailin-rebate value from the supply chain perspective, see Scenario 3), beyond which the
wholesale price discount performs better. The above behaviour occurs because the gain in
profit for the SC due to the increase in demand is less than the rebate provided to the endconsumer.
In the next section we design the combined rebate mechanism.
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7.5 Combined rebate mechanism
In the so-called combined rebate mechanism the Buyer provides a rebate R to the endconsumer, and after ensuring the Buyer’s action with respect to the rebate, the Supplier
provides a wholesale price discount d to the Buyer. In this analysis we test whether the
combined rebate mechanism has the potential to coordinate and provide win-win
opportunities for the players and we compare its performance to the mail-in-rebate
mechanism.
Under the combined rebate mechanism (described by subscript 5) we assume the events
to take place in the following sequence:
1) The Supplier initially fixes the wholesale price as in the solitaire scenario;
2) Given the wholesale price the Buyer decides the final selling price (which, again,
is the same as in the solitaire scenario);
3) The Supplier and Buyer come to an agreement on the combined rebate contract
[d5;R5], i.e., decide on two rebate values simultaneously: one given by the
Supplier to the Buyer (d5) and the other given by the Buyer to the end-consumer
(R5).
The underlying idea of the proposed combined rebate mechanism is that the rebate
provided by the Buyer to the end-consumer will increase the demand but decreases the
Buyer’s profit. The Supplier receives a greater profit because of the higher consumer
demand. If the Supplier is willing to compensate the Buyer for his loss and enable the
Buyer to make some extra profit when compared to the solitaire scenario then it might be
possible to encourage the Buyer to provide a rebate that is optimal for the SC.
The profit for the Supplier, Buyer and the SC under the combined rebate mechanism can
be obtained as:
S 5 : W1* c Q5 d 5 Q5 ;
B5 :
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P
*
1
c Q5 d 5 Q5 R5Q ; and
(7.37)
(7.38)
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T5 :
P
*
1
c R5 Q5 .
173
(7.39)
The following theorem shows the key results of the combined rebate mechanism.
Theorem 7.2
There are values of d5 and R5* within the combined rebate contract [d5; R5* ] such that
under the combined rebate mechanism:
(i)
the SC is coordinated ;
(ii)
both the Buyer and the Supplier have a higher profit than under the solitaire
scenario;
(iii)
both the Buyer and the Supplier have a higher profit than under the mail-inrebate mechanism.
Proof
(i) Assume that the rebate value is set equal to the rebate value that optimizes the SC.
Using Equation (7.39) it then follows that:
1
D Ec .
4E
R5*
(7.40)
When the Buyer provides the rebate value as obtained in Equation (7.40), the price that
the end-consumer has to pay for the product can be obtained as:
P1* R5*
P5*
D Ec
.
2E
(7.41)
D Ec .
(7.42)
It follows that the order size is given by:
Q5*
D EP5
1
2
After the Buyer fixes the final selling price and the rebate value, the Supplier has to
decide on the wholesale price rebate d5 he will provide to the Buyer. The profit for the
players and the SC can be obtained as:
S 5 (d 5 )
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4
– 1
(D Ec)d 5 ;
4 2
(7.43)
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CHAPTER
B5 (d 5 )
1
2
(D Ec)d 5 ; and
T5
–.
7
(7.44)
(7.45)
As can be seen from Equation (7.45), the SC profit is optimal, i.e., the SC is coordinated,
independent of what value is chosen for d5.
(ii) From S1
–
and Equation (7.45) it follows that S5 ! S1 iff:
2
d5 Furthermore, from B1
(D Ec)
.
4E
(7.46)
–
and Equation (7.44) it follows that B5 ! B1 iff:
4
d5 !
(D Ec)
.
8E
(7.47)
It can be concluded that win-win is achieved with the combined rebate mechanism when
compared to the solitaire scenario when:
(D Ec)
(D Ec)
d5 .
8E
4E
(7.48)
(iii) From Equations (7.17) and (7.43) it follows that S5 ! S 2 iff:
d5 7(D Ec)
.
32E
(7.49)
Also, from Equations (7.16) and (7.42) if follows that B5 ! B2 iff:
d5 !
3(D Ec)
.
16 E
(7.50)
It can be concluded that the combined rebate mechanism provides win-win compared to
the mail-in-rebate mechanism iff:
6(D Ec)
7(D Ec)
d5 .
32E
32E
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(7.51)
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USING PROMOTION MECHANISMS TO COORDINATE DECISIONS IN A SUPPLY CHAIN WITH PRICE SENSITIVE DEMAND
This completes the proof.Ŷ
It can be concluded that the combined rebate mechanism provides both coordination and
win-win. Moreover, the combined rebate mechanism outperforms the mail-in-rebate
mechanism in terms of profit for the Buyer and Supplier. In that sense the combined
rebate mechanism is superior to the mail-in-rebate mechanism.
Example (continued)
Under the combined rebate mechanism R5 is set equal to 5. When 2.5 d d 5 d 5 , the
combined rebate mechanism provides win-win when compared to the solitaire scenario.
If 3.75 d d 5 d 4.375 the combined rebate mechanism provides win-win when compared to
the mail-in-rebate mechanism. Assuming d5 = 4, the results for the numerical example are
summarized in Table 7.4.Ŷ
No. Scenario
R
D
W
P
Q
B
S
T
0
Centralized
n/a
n/a
n/a
40
20
n/a
n/a
200
1
Solitaire
n/a
n/a
40
45
10
50
100
150
2
Mail-in-rebate
2.5
n/a
40
45-2.5
15
75
112.5
187.5
5
4
40
45-5
20
80
120
200
Supplier opt
5
Combined
rebate
Table 7.4: Combined rebate mechanism results (numerical example)
In the next section we conclude our study and provide some managerial insights.
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7.6 Conclusions
The analysis in this chapter has led to the following insights:
1. When the Supplier provides a mail-in-rebate which is optimal for him, the SC does
not coordinate, but win-win is achieved;
2. When the Supplier chooses a rebate value which is optimal for the SC, the SC is
coordinated but the Supplier makes the same profit as in the solitaire scenario, hence
win-win in the strong sense is not achieved;
3. The wholesale price mechanism’s performance is inferior to that of the mail-in-rebate
mechanism. In fact, the Supplier and the SC make lower profits when compared to
the solitaire scenario. However, the Buyer benefits to a greater degree when
compared to the solitaire scenario with the wholesale price discount.
4. The combined rebate mechanism can achieve both coordination and win-win. In that
sense it is superior to the mail-in-rebate mechanism.
For future research many extensions of the basic model are of interest. Just a few
examples are: testing the combined rebate mechanism in a setting where there is
asymmetry of information between the Supplier and the Buyer (i.e., the Buyer knows the
end-consumer demand with a greater certainty than the Supplier); including uncertain
(stochastic) demand; and including competition at the Buyer and/or Supplier level.
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Part 3: Contract Mechanisms for Coordinating Price and
Service-level Decisions in a Supply Chain
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Chapter 8
Coordinating Mechanisms for a Supply Chain Facing Price and Servicelevel Sensitive Demand 8
Chapter Synopsis
In this chapter, a two stage SC (consisting of a Buyer and a Supplier) in which the endconsumer demand is influenced by the price of the product and by the service-level
provided at the Buyer’s outlet is considered. Two different scenarios are considered: one
in which the Buyer makes the service-level decision and the other in which the Supplier
makes the service-level decision. In both scenarios, it is assumed that the player who
makes the service-level decision also incurs the cost associated with the chosen service
provision.
First, it is shown that in this setting a decentralized SC results in sub-optimal solutions for
both decision variables (price and service-level). No matter which player in the SC is
providing the service, a lower service-level is provided and a higher price is charged in a
decentralized SC when compared to a centralized SC.
Four contract mechanisms, namely the revenue sharing, profit sharing, quantity discount
and the license fee mechanism, are designed in both settings with the following results.
The revenue sharing mechanism coordinates the pricing decision but not the service-level
decision for all values of the cost of service provision. However, win-win opportunities
are achieved for the entire range of the cost of service provision. The profit sharing,
quantity discounts and license fee mechanisms are shown to coordinate the pricing and
service-level and also provide win-win opportunities for the entire range of the cost of
service provision.
8
This chapter is the modified version of the paper presented at the 15th International EurOMA conference
at Groningen in June 2008[Reference: Nalla, V. R, J.A.A van der Veen, and V. Venugopal (2008)].
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8.1 Introduction
At a large consumer electronics retailer, the consumer demand for any product is
dependent not only on price but also on the quality of (sales) service provided within the
store. Particularly for electronic products, in-store sales personnel must have adequate
product knowledge to aid customers in making purchase decisions, see for example
Cachon (2003). This can be achieved by hiring more sales people and/or improving their
skills through training. Sales can also be increased by:
a) increased advertising;
b) better maintenance of the attractiveness of the product’s display;
c) enhancing the ambience of the store interior (e.g., richer materials, wider aisles);
d) giving the product a better stocking location within the store.
Depending on the product category, the retailer will have to take a few or all of the above
actions. In this study, we assume that the combination of the above factors, which we call
the service-level, is valued by the consumers and will therefore have a positive impact on
the end-consumer demand. Clearly, all of these activities are costly. As a result, a conflict
exists between the manufacturer (Supplier) and the retailer (Buyer) no matter what level
of effort the Buyer dedicates towards those activities, the Supplier prefers that the Buyer
exert even more effort. However, those activities benefit both firms in terms of increased
sales, but are costly to only one. Due to this, a SC optimal level of service at the retail
outlet is not generally observed.
Sharing the cost of the sales effort is one solution to the above coordination problem. For
example, the Supplier could pay some of the Buyer’s advertising expenses, or could
compensate the Buyer a portion of the training costs. However, many situations exist in
which cost-sharing is not effective for the Supplier. This happens for instance when an
advertisement merely promotes the Buyer’s brand image and enhances the demand for all
of the Buyer’s products, not just the Supplier’s product, see also Cachon (2003). In this
chapter, contracts are designed to address the issues of coordination and providing win-
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win opportunities when the Buyer provides the service at a cost and this service has a
positive influence on the end-consumer demand.
It is also possible for the Supplier to choose to provide the service at the Buyer’s site. We
can cite numerous real life examples where the manufacturer chooses to provide service
at the retailer outlet. Soft drink companies such as Coca Cola and PepsiCo provide the
Buyer with retail equipment (refrigerators/vending machines, et cetera) with special
company labels and logos and expect the Buyer to carry only their product brand. This
increases the product availability, demands special attention from the consumers and has
a positive influence on demand. These companies can also provide the Buyer with special
advertising posters of their brands and ensure that these posters are displayed at
appropriate places, therefore enhancing demand for their products. Another interesting
example is that of Dutch real estate owners who specialize in building shopping malls
which would accommodate factory outlets for all top brand manufacturers at one
location. These builders/real estate owners take care of ambience, catering, and also take
the initiative in the marketing of the shopping mall. These efforts will be taken up by the
outlet renters to create a good experience for the consumers, which will have a positive
impact on demand. The benefit for the renters is that the retailers share a part of their
revenues with the renters.
This study designs four contracts (revenue sharing, profit sharing, quantity discount and
license fee) to address the issues of coordination and providing win-win opportunities
when the Supplier provides the service at the Buyer’s outlet and incurs the cost associated
with providing that service.
The literature addresses a few studies on coordinating sales effort decisions. However,
the model and treatment of the problem in these papers is very different from what we
have done in this study. Nettessine & Rudi (2000) present a coordinating contract, which
involves sharing advertising costs in a newsvendor model setting, in which the demand is
influenced by the Buyer’s effort. In Wang & Gerchak (2001), the Buyer’s shelf space has
been considered an effort variable. They also allow the Supplier to compensate the
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8
retailer for his effort, which in their model takes the form of an inventory subsidy. Gilbert
& Cvsa (2000) study a model in which additional sales effort is observable but not
verifiable.
Our model resembles the one discussed in Raju & Zhang (2005), with the exception that
we do not consider competition and the dominant Buyer concept. Raju & Zhang (2005)
show that the quantity discounts and two-part tariff coordinate the SC, and also provide
conditions under which the quantity discount contract is better than a menu of two-part
tariffs. We add a new dimension of different players being able to provide the service,
and test all the four contract mechanisms a setting where the Supplier provides service at
the Buyer’s outlet.
The remainder of this chapter is organized as follows. In the next section the model is
analyzed in the centralized scenario. Subsequently, we analyze the model in the
decentralized scenario (when the Buyer makes the service-level decision) and design the
coordination mechanisms in this setting. Next, the results for the case in which the
Supplier makes the service decision are presented. Finally, we conclude the study and
provide some directions for further research.
8.2
Model in which the Buyer decides the level of service provision
Consider the situation in which the Supplier offers a quantity Q of a product to the Buyer
at a price of W per unit. It is assumed that the product has a short life cycle, with only a
one-time order placed by the Buyer (i.e., reordering is not possible and there is no stock
from previous periods). The manufacturing and transportation costs for the Supplier are
normalized to zero for the simplicity of analysis. Relaxing this assumption would not
impact our results. It is also assumed that the Buyer and Supplier are fully informed of
the demand function and the costs incurred by each player. Furthermore, it is assumed
that the final customer demand D for the product depends both on the price P set by the
Buyer and on the service-level K provided at the Buyer’s outlet. The service-level is
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normalized such that 0 d K d 1 . In it simplest form, the end-consumer demand linearly
decreases with price and increases with the level of service provided at the Buyer’s outlet,
i.e.,
D ( P , K ) D E P KK
(8.1)
with D, E, Ș > 0. Clearly, K is a parameter that represents the maximum level to which
the demand can be increased by improving the service-level. The service provision comes
at a cost (represented by f), and this cost of service provision is proportional to the level
of service provided. Once the Buyer sets the price P and the service-level K, he can
determine the demand D and place an order of size Q = D(P,K) with the Supplier. The
SC described above is depicted in Figure 8.1.
Q
Q
Q Q
Supplier
Supplier
(Decides
:W):W)
(Decides
W
W
Buyer
Buyer
(Decides
,.Κ )
(Decides :P
: P,
.
Κ
P P
Customer
Customer
DD
( P()P=) α −
D βPE+PηK
KK
Figure 8.1: SC Structure when the Buyer decides the service-level provided
The profits for the Buyer, Supplier and the SC can be obtained as:
B
(D EP KK )( P W ) Kf ;
(8.2)
(D EP KK )W ; and
(8.3)
S
T
BS
(D EP KK ) P Kf
(8.4)
respectively.
In the next section, we perform the centralized scenario analysis.
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8.3 Centralized scenario
A centralized SC will choose the price and service-level which will optimize the SC
profit. Since this is the first scenario considered, the relevant decision variables will be
indicated with a subscript 0. The SC profit can be denoted as:
T0 ( P0 , K 0 ) (D EP0 KK 0 ) P0 K 0 f .
(8.5)
Partially differentiating Equation (8.5) with respect to P0 and equating it to zero gives
the value of P0 that will optimize the SC profit. The optimal selling price is obtained as:
P0*
D KK0
.
2E
(8.6)
Using Equation (8.1) and the selling price in Equation (8.6) gives us the optimal order
quantity:
D0 ( P0* , K 0 )
1
2
D KK .
0
(8.7)
Substituting the value of P0* in Equation (8.5) yields the following SC profit:
T0 ( P0* , K 0 )
(D KK 0 ) 2
K0 f
4E
(8.8)
Please note that the second derivative of Equation (8.8) with respect to K 0 is positive.
This indicates a minimum SC profit for the value of K 0 at which its first derivative is
equal to zero. In fact, Equation (8.8) is a quadratic expression of convex nature and will
achieve its maximum at the extreme value of the feasible range for K 0 . The extreme
values of K 0 are 0 and 1 (by definition) and therefore it is sufficient to test the SC profit
at these values of K 0 :
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T0 ( P0* ,0)
D2
; and
4E
T0 ( P0* ,1)
(D K ) 2
f.
4E
(8.9)
(8.10)
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It follows that a centralized SC would choose a value of K0 = 1 when the SC profit in
Equation (8.10) is greater than the profit obtained in Equation (8.9), i.e., iff:
f d
K (K 2D )
.
4E
(8.11)
Equation (8.11) gives an upper bound for the cost of service provision, below which an
integrated SC would be willing to provide full service. Whenever the condition on f in
Equation (8.11) is not fulfilled, then the centralized SC opts to provide no service (i.e., K0
= 0). Summarizing, it can be concluded that:
If f d
K (K 2D )
,
4E
then P0*
(D K )
;
2E
K 0*
1 with SC profit T0
(D K ) 2
f ;
4E
K (K 2D )
,
4E
then P0*
D
;
2E
K 0*
0 with SC profit T0
D2
f.
4E
and
if f t
Example
To provide more insight into the results for the various scenarios, we consider three
different numerical examples throughout this paper.
In Example [1], we consider D
D
100; E
2;K
20; f
100; E
2;K
20; f
300 ; and for Example [3], D
200 ; for Example [2],
100; E
2;K
20; f
600 .
With these parameter values the centralized channel will provide full service
when f d 550 . In Example [1], f = 200 < 550 which leads to the unique optimal solution
P0*
30 and K 0*
1 with a SC profit of T0
leads to the unique optimal solution P0*
1600 . In Example [2], f = 300 < 550 which
30 and K 0* 1 with SC profit T0
1500 .
Finally, in Example [3], f = 600 > 550 which leads to the unique optimal solution
P0*
25 and K 0*
0 with SC profit T0
1250 .Ŷ
In the next section we analyze the solitaire scenario.
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8.4
CHAPTER
8
Solitaire Scenario analysis (decentralized channel)
In a decentralized SC (also called the solitaire scenario), each player will choose levels
for the decisions under his control which would maximize his own profits. As mentioned,
the Buyer decides on the final selling price and on the level of service he will provide,
and the Supplier decides on the wholesale price. The profit for the Buyer, Supplier and
the SC can be obtained as (where the subscript 1 refers to the solitaire scenario):
B1
(D EP1 KK1 )( P1 W1 ) K1 f ,
(8.12)
(D EP1 KK1 )W1 ; and
(8.13)
S1
T1
B1 S1
(D EP1 KK1 ) P1 K1 f
(8.14)
respectively.
The following theorem summarizes the main results for the solitaire scenario.
Theorem 8.1
(i)
In a decentralized SC, the Buyer fixes the final price at a higher level and orders
a lower quantity when compared to the centralized SC. As a result, this leads to a
lower profit for the entire SC.
(ii)
If
K (K 2D )
K (K 2D )
d f d
, then the Buyer in a decentralized SC would
16E
4E
choose to provide no service, whereas in the centralized channel full service
would be provided.
Proof
(i) From Equation (8.12) the value of P1 that will optimize the Buyer’s profit is given by:
P1
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D KK 1 E W1
.
2E
(8.15)
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The Supplier uses the Buyer’s optimal selling price to maximize his profit. Substituting
P1 from Equation (8.15) in (8.13) and obtaining the first order condition with respect to
W1 gives:
D KK 1
.
2E
W1*
(8.16)
Substituting W1* from Equation (8.16) in (8.15) gives the Buyer’s optimal selling price
as:
P1*
3(D KK1 )
.
4E
(8.17)
Comparing Equation (8.6) & Equation (8.17) it can be observed that the Buyer’s selling
price is 1.5 times the Supplier’s selling price chosen in a decentralized situation
( P1
1.5 P0* ) . The order size is given by:
Q1*
1
4
D KK .
1
(8.18)
Comparing Equation (8.7) & Equation (8.18) it can be observed that the ordered quantity
in the decentralized scenario is reduced to half when compared to the centralized scenario
( Q1*
0.5Q0* ). Using P1* from Equation (8.17), the SC profit in the decentralized channel
can be obtained from Equation (8.14) as:
T1
3(D K1K ) 2
K1 f .
16 E
(8.19)
The difference in the SC profit in the centralized and the decentralized channel can be
obtained from Equations (8.8) and (8.19) as:
T0 T1
(D K1K ) 2
.
16E
(8.20)
Since the value in Equation (8.20) is always positive for any feasible value of the service
provision K1 we can conclude that the resulting SC profit in the decentralized channel is
lower.
(ii) The Buyer’s profit with the selling price and the ordered quantity values as obtained
in Equations (8.17) and (8.18) is:
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CHAPTER
B1
(D KK1 ) 2
K1 f .
16 E
8
(8.21)
As before, it can be noted that the Buyer’s profit is a convex function with respect to K1 ,
i.e., the function will achieve its maximum at the extreme value of the feasible range
for K1 . It follows that:
If K1
0 then:
if K1
1 then:
D2
16 E
B1
; and
(8.22)
(D K ) 2
f .
16 E
B1
(8.23)
1 when the profit in Equation (8.23) is
Clearly, the Buyer will choose a value of K1
greater than the profit in Equation (8.22), i.e., iff:
f d
K (K 2D )
.
16E
(8.24)
Equation (8.24) gives an upper bound for the cost of service provision, below which the
Buyer will provide full service (i.e., K0 = 1). Whenever the condition on f in Equation
(8.24) is not fulfilled, then the Buyer in the decentralized scenario will decide not to
provide any service (i.e., K1 = 0). We conclude that the Buyer will choose to provide full
service if and only if the inequality in Equation (8.24) is fulfilled.
Summarizing:
f !
if
K (K 2D )
, then K 1*
16E
B1
f if
f
3D
; W1*
4E
D2
; S1
16 E
K (K 2D )
, then K1* 1 ; P1*
16E
B1
if
0 ; P2*
2D 2
; T1
16 E
3(D K )
; Q1*
4E
(D K ) 2
f ; S1
16 E
D
2E
; Q1*
D
4
3D 2
;
16E
(D K )
; W1*
4
(D K ) 2
; T1
8E
(D K )
;
2E
3(D K ) 2
f
16E
K (K 2D )
, then both mentioned solutions are optimal.
16E
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189
Using Equations (8.11) and (8.24) a range for the cost of service provision for which a
centralized SC would provide full service and a decentralized SC would choose to
provide no service is shown to be:
K (K 2D )
K (K 2D )
d f d
.
16E
4E
(8.25)
This completes the proof.Ŷ
Figure 8.2 depicts the performance of the SC under the centralized and decentralized
scenario and indicates the region that needs to be coordinated.
No service K=0
Full service K=1
f f
Centralized channel
T
(D K ) 2
f
4E
T
(D K ) 2
f
4E
T
D2
4E
No service K=0
Full service K=1
f f
Decentralized channel
T
3(D K ) 2
f
16E
Double marginalization on price only
T
3D 2
16E
Double marginalization on price and service
K (K 2D )
16 E
3D
16E
2
T
Double marginalization on price only
K (K 2D )
4E
Figure 8.2: Performance of the decentralized channel vs. the centralized channel
It can be seen from Figure 8.2 that if the cost of service provision is low
(f d
K (K 2D )
), then both the centralized and the decentralized channels provide full
16E
service. However, the SC profit is lower in the decentralized channel as compared to the
centralized channel. It can be concluded that in this case only the pricing decision needs
to be coordinated. When the cost of service provision is in the “middle” (more
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CHAPTER
specifically, if
8
K (K 2D )
K (K 2D )
d f d
), then the decentralized channel does not
16E
4E
provide service, whereas providing full service would be optimal for the coordinated SC.
This implies that there is double marginalization on both price and service for these
values of the service cost parameter. In other words, both of these decisions are to be
coordinated. When the cost of service is relatively high ( f t
K (K 2D )
), both the
4E
centralized and decentralized channels provide no service. Again, the SC profit is lower
in the decentralized channel when compared to the centralized channel, so here also only
the pricing decision needs to be coordinated.
Example (continued)
Returning to the numerical examples, it can be concluded that the Buyer in a
decentralized channel will provide full service when f d 137.5 . In Example [1], f = 200>
137.5, giving the unique optimal solution of P1*
T1
is P1*
937.5 T0
37.5 and K1*
937.5 T0
0 with SC profit
1600 . For Example [2], f = 300 > 137.5 so the unique optimal solution
0 with SC profit T1
937.5 T0
137.5 with the unique optimal solution of P1*
= T1
37.5 and K1*
1500 . In Example [3], f = 600 >
37.5 and K1*
0 with SC profit
1250 . In all three examples, the profit for the Buyer is 312.5 and that
of the Supplier is 625. Moreover, in all three examples the SC profit in the decentralized
channel is lower than in the centralized channel.Ŷ
In the next section, we design different contracts to test their ability to coordinate both the
pricing and service-level decisions when the decentralized channel does not do so. These
mechanisms are designed with an objective of providing both coordination and win-win
opportunities.
We design four different contracts, namely the revenue sharing, profit sharing, quantity
discount, and license fee mechanisms to achieve coordination and win-win opportunities.
In the next section we design the revenue sharing mechanism.
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8.5
191
Revenue sharing mechanism
In the revenue sharing mechanism, the transactions between the Supplier and the Buyer
are governed by the Supplier receiving a share of the Buyer’s revenues. The revenue
sharing mechanism can be identified by two parameters, namely the wholesale price W
and a percentage of the Buyer’s profit J (0 < J < 1) that goes to the Supplier. Under the
revenue sharing mechanism (denoted by subscript 2), the profit for the Buyer, Supplier
and SC is obtained as:
B2 (Q2 , K 2 ) (1 J 2 ) P2 Q2 W2 Q2 K 2 f ;
(8.26)
S 2 (Q2 , K 2 ) J 2 P2 Q2 W2 Q2 ; and
(8.27)
T2 (Q2 , K 2 )
respectively, where Q2
P2 Q2 K 2 f
(8.28)
D EP2 KK 2 .
The following theorem summarizes the key results for the revenue sharing mechanism.
Theorem 8.2
(i)
There is a revenue sharing contract [W2* , J 2 ] such that the SC is coordinated if and
only if either f d (1 J 2 )
(ii)
K (K 2D )
K (K 2D )
or f t
.
4E
4E
For all f there is a revenue sharing contract [W2* , J 2 ] such that win-win
opportunities are achieved.
Proof
(i) Clearly, the Buyer will choose the value of Q2 that optimizes his profit. This value is
obtained by calculating the first order conditions for Equation (8.26). It follows that the
Buyer’s optimal value of Q2 is:
Q2*
(D KK 2 )(1 J 2 ) W2 E
.
2(1 J 2 )
(8.29)
Recall that the optimal Q0 from the centralized scenario from Equation (8.4) is:
Inside_proefschrift_Vijayender_06.indd 191
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CHAPTER
Q0*
D KK 0
2
.
8
(8.30)
From Equations (8.29) and (8.30), it is clear that the Buyer’s optimal order quantity
coincides with the optimal SC order quantity when W2 = 0. We therefore consider a
revenue sharing contract [W2 , J 2 ] where W2*
0 in order to achieve coordination. The
optimal price and the order quantity with the revenue sharing contract [W2*
obtained as: P2*
1
2E
D KK 2 ; and
Q2*
1
2
0, J 2 ] can be
D KK 2 . The profits for the Buyer, Supplier
and the SC with the revenue sharing mechanism can now be obtained as:
§ (D KK 2 ) 2 ·
¸¸ K 2 f ;
B2 ( K 2 , J 2 ) (1 J 2 )¨¨
4E
©
¹
(8.31)
§ (D KK 2 ) 2 ·
¸¸ ; and
S 2 (J 2 ) J 2 ¨¨
4E
©
¹
(8.32)
T2
§ (D KK 2 ) 2 ·
¨¨
¸¸ K 2 f .
4E
©
¹
(8.33)
The Buyer’s profit when he provides no service with the revenue sharing contract can be
obtained as:
B2 (0, J 2 )
§D2 ·
¸¸ .
(1 J 2 )¨¨
© 4E ¹
(8.34)
The Buyer’s profit when he provides full service with the revenue sharing contract is
given by:
§ (D K ) 2 ·
¸¸ f .
B2 (1, J 2 ) (1 J 2 )¨¨
© 4E ¹
(8.35)
The Buyer will choose to provide full service (K2 = 1) when this generates a higher profit
compared to providing no service (K2 = 0), i.e., iff:
§ K (K 2D ) ·
¸¸ .
f d (1 J 2 )¨¨
4E
©
¹
(8.36)
It can be concluded that:
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if
§ K (K 2D ) ·
¸¸ , then K 2* 1 ; P2*
f d (1 J 2 )¨¨
4
E
©
¹
§ (D K ) 2 ·
¸¸ f ; S 2
(1 J 2 )¨¨
© 4E ¹
B2
if
§ K (K 2D ) ·
¸¸ ,
f ! (1 J 2 )¨¨
4E
©
¹
§D2
(1 J 2 )¨¨
© 4E
B2
(D K )
; Q2*
2E
§ (D K ) 2 ·
¸¸ ; T2
© 4E ¹
0 ; P2*
§D2
© 4E
·
¸¸ f ; S 2
¹
(D K )
2
§ (D K ) 2 ·
¨¨
¸¸ f ;
© 4E ¹
J 2 ¨¨
then K 2*
J 2 ¨¨
D
; Q2*
2E
§D2
¨¨
© 4E
·
¸¸ ; T2
¹
193
D
2
·
¸¸ f .
¹
It is clear from Equation (8.36) that the region for service coordination is dependent on
the parameter J 2 , i.e., the service-level coordination with the revenue sharing mechanism
is dependent on the revenue sharing parameter. The performance of the revenue sharing
mechanism over the various cases is summarized in Figure 8.3.
Region 1
Region 2
Region 4
Region 3
Noservice
serviceK=0
K=0
No
Full
Fullservice
serviceK=1
K=1
Centralized channel
(D K ) 2
f
4E
T
T
(D K ) 2
f
4E
T
D2
4E
ff
No service K=0
Full service K=1
Full service K=1
ff
Revenue sharing
T
(D K ) 2
f
4E
T
D2
4E
No service K=0
Full service K=1
Full service K=1
f
Decentralized channel
T
3(D K ) 2
f
16E
T
K (K 2D )
16 E
(1 J 3 )
K (K 2D )
4E
3D 2
16E
K (K 2D )
4E
Figure 8.3: Performance of the centralized channel, revenue sharing and decentralized
channel
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CHAPTER
8
As can be seen from Figure 8.3, the revenue sharing mechanism coordinates the service
decision in Regions 1 and 2 (i.e., when f d (1 J 2 )
K (K 2D )
). However, the revenue
4E
sharing mechanism provides no service in Region 3 (which is defined as
(1 J 2 )
K (K 2D )
K (K 2D )
d f d
), whereas the centralized channel provides full
4E
4E
service. In Region 4 ( f t
K (K 2D )
), both the centralized channel and the channel with
4E
revenue sharing lead to a situation in which no service is provided. As can be
immediately seen from the SC profits given in Figure 8.3, the SC is coordinated in
Regions 1, 2 and 4. However, the SC profit in Region 3 under the revenue sharing
scenario is lower than in a centralized channel.
(ii) In order to prove the second part of the theorem, win-win opportunities need to be
achieved in all four regions of Figure 8.3.
Region 1: The Buyer’s profit in the decentralized scenario in Region 1 is equal to
§ (D K ) 2 ·
¨¨
¸¸ f . Revenue sharing therefore provides a higher profit to the Buyer when
© 16 E ¹
compared to the solitaire scenario iff:
§ (D K ) 2 ·
§ (D K ) 2 ·
¸¸ f ! ¨¨
¸¸ f ;
(1 J 2 )¨¨
© 4E ¹
© 16E ¹
i.e., iff:
J 2 34 .
(8.37)
§ (D K ) 2 ·
¸¸ . Therefore,
The Supplier’s profit in the decentralized situation in Region 1 is ¨¨
© 8E ¹
revenue sharing provides a higher profit to the Supplier when compared to the solitaire
scenario iff:
§ (D K ) 2 · § (D K ) 2 ·
¸¸ ! ¨¨
¸¸ ,
© 4 E ¹ © 8E ¹
J 2 ¨¨
which is equivalent to:
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J 2 12 .
195
(8.38)
It can be concluded that win-win is achieved in Region 1 when:
1
2
J2 3
4
.
§ D2 ·
¸¸ , so
Region 2: The Buyer’s profit in the decentralized situation in Region 2 is ¨¨
© 16 E ¹
revenue sharing provides a higher profit to the Buyer in Region 2 when:
§ (D K ) 2 ·
§ 2 ·
¸ f ! ¨ D ¸,
(1 J 2 )¨
¨ 16E ¸
¨ 4E ¸
¹
©
©
¹
which is equivalent to:
§ D 2 16Ef
2
© 4(D K )
J 2 1 ¨¨
·
¸¸ : (J 2 ) .
¹
(8.39)
§D 2 ·
¸¸ . The revenue
The Supplier’s profit in the decentralized situation in Region 2 is ¨¨
© 8E ¹
sharing provides a higher profit to the Buyer in Region 2 when compared to the solitaire
scenario iff:
§ (D K ) 2 · § D 2 ·
¸¸ ,
¸¸ ! ¨¨
© 4 E ¹ © 8E ¹
J 2 ¨¨
i.e., iff:
·
§ D2
¸ : (J 2 ) .
J 2 ! ¨¨
2 ¸
D
K
2
(
)
¹
©
(8.40)
Win-win opportunities are achieved in Region 2 iff: (J 2 ) (J 2 ) ! 0 , i.e., iff:
§ K (K 2D ) · § D 2 ·
¸¸ .
¸¸ ¨¨
f ¨¨
4E
©
¹ © 16E ¹
(8.41)
Clearly this inequality holds in Region 2, so it can be concluded that win-win
opportunities are achieved in Region 2 when:
§ D 2 16Ef
·
§ D2
¨¨
¸
¨¨
J
1
2
2 ¸
2
© 4(D K )
© 2(D K ) ¹
Inside_proefschrift_Vijayender_06.indd 195
·
¸¸ .
¹
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196
CHAPTER
8
Regions 3 and 4: The Buyer’s profit in the decentralized situation in Regions 3 and 4 is
§ D2
¨¨
© 16 E
·
¸¸ . The revenue sharing provides a higher profit to the Buyer in these regions when
¹
compared to the solitaire scenario iff:
§D2 · § D2 ·
¸¸ ! ¨¨
¸¸ ;
(1 J 2 )¨¨
© 4E ¹ © 16E ¹
which is equivalent to:
J 2 34 .
(8.42)
§ D2
The Supplier’s profit in the decentralized situation in Regions 3 and 4 is ¨¨
© 16 E
·
¸¸ . Hence,
¹
the revenue sharing provides a higher profit to the Supplier in these regions when
compared to the solitaire scenario iff:
§D2 · §D2 ·
¸¸ ! ¨¨
¸¸ ;
© 4 E ¹ © 8E ¹
J 2 ¨¨
i.e., iff:
J2 1
2
.
(8.43)
It can be concluded that win-win opportunities are achieved in Regions 3 and 4 when
1
2
J2 3
4
.
Since win-win opportunities are available in all four regions this concludes the proof. Ŷ
Example (continued)
In the numerical example, the revenue sharing mechanism coordinates the service-level
decision when f d (1 J 2 )550 . Assuming J 2
when f d 206 . In Example [1], f
5
8
, the Buyer provides full service
200 (which falls in Region 2) so the Buyer and the
centralized channel will provide full service. Both the pricing and service-level decisions
are coordinated. The profits for the Buyer, Supplier and the SC can be obtained as 700,
900 and 1600, respectively. The Buyer and the Supplier make greater profits when
compared to the decentralized channel (a win-win situation is achieved).
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For Example [2], since f
197
300 (which falls in Region 3), the Buyer will provide no
service whereas the centralized channel will provide full service. Here the pricing
decision is coordinated but the service-level is not. The profits for the Buyer, Supplier
and the SC can be obtained as 469, 781 and 1250, respectively. Both the Buyer and the
Supplier make greater profits than in the decentralized channel (win-win is achieved),
however the SC is not coordinated.
For Example [3], since f
600 (which falls in Region 4), the Buyer and the centralized
channel will provide no service. Both the pricing and the service-level decisions are
coordinated. The profits for the Buyer, Supplier and the SC can be obtained as 461, 781
and 1250, respectively. Both the Buyer and the Supplier make greater profits than in the
decentralized channel (win-win is achieved), and the SC is coordinated.Ŷ
8.6
Profit Sharing
The profit sharing mechanism can be identified by two parameters, namely the wholesale
price W and a percentage of the Buyer’s profit G (0< G <1) that goes to the Supplier. Let
the subscript 3 denote the profit sharing mechanism. The profit for the Buyer with the
profit sharing mechanism can be obtained as:
B3 (Q3 ,W3 , K 3 ) (1 G 3 )P3Q3 W3 Q3 K 3 f ;
(8.44)
S 3 (Q3 ,W3 , K 3 ) (1 G 3 )P3Q3 W3 Q3 K 3 f W3 Q3 ; and
(8.45)
T3 (Q3 ,W3 , K 3 )
respectively, where Q3
P3Q3 K 3 f
(8.46)
D EP3 KK 3 .
The following theorem discusses the potential of the profit sharing mechanism to provide
coordination and win-win opportunities.
Theorem 8.3
For all f there is a profit sharing contract [W3* , G 3 ] such that:
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CHAPTER
(i)
the SC is coordinated
(ii)
win-win opportunities are achieved.
8
Proof
(i) Obviously, the Buyer chooses the order size that optimizes his profit. The optimal
order size can be obtained by finding the first order conditions for Equation (8.44), i.e.,
the Buyer’s optimal order size Q3 is:
Q3
1
2
(D KK ) W E .
3
(8.47)
3
Since the optimal order size in the centralized scenario is Q0*
1
2
D KK 0 ,
it follows that the Buyer’s optimal order size is equal to the SC optimal order size when
W3 = 0. Therefore, we will now consider a profit sharing contract [W3* , J 3 ] where
W3*
0 . Under such a contract, the profits for the Buyer, Supplier and SC are given by:
§ (D KK 3 ) 2
B3 (G 3 ) (1 G 3 )¨¨
K3 f
4E
©
§ (D KK 3 ) 2
S 3 (G 3 ) G 3 ¨¨
K3 f
4E
©
T3
·
¸¸ ;
¹
(8.48)
·
¸¸ ; and
¹
(8.49)
§ (D KK 3 ) 2 ·
¨¨
¸¸ K 3 f .
4E
©
¹
(8.50)
The Buyer’s profit when he provides no service with the profit sharing contract is given
by:
§D2 ·
¸¸ .
B3 (0, G 3 ) (1 G 3 )¨¨
© 4E ¹
(8.51)
The Buyer’s profit when he provides full service with the profit sharing contract is given
by:
§ (D K ) 2
·
B3 (1, G 3 ) (1 G 3 )¨¨
f ¸¸ .
© 4E
¹
Inside_proefschrift_Vijayender_06.indd 198
(8.52)
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199
Using Equations (8.51) and (8.52), it can be seen that the Buyer will provide full service
iff:
f d
K (K 2D )
.
4E
(8.53)
It can therefore be concluded that:
if f d
K (K 2D )
, then K 1 ; P3*
4E
B3
if
f !
(D K )
; Q3*
2E
§ (D K ) 2
·
f ¸¸ ; S 3
(1 G 3 )¨¨
© 4E
¹
K (K 2D )
, then K
4E
0 ; P3*
§D2
(1 G 3 )¨¨
© 4E
B3
(D K )
2
(D K ) 2
f ; and
4E
§ (D K ) 2
·
f ¸¸ ; T3
© 4E
¹
G 3 ¨¨
D
2E
·
¸¸ ; S 3
¹
D
; Q3*
2
§D2 ·
¸¸ ; T3
© 4E ¹
G 3 ¨¨
D2
.
4E
As is immediately clear from Equation (8.53), the region for service coordination in this
profit sharing scenario is the same as that in the centralized scenario. In other words, the
profit sharing mechanism coordinates both the pricing and service-level decisions. The
performance of the profit sharing mechanism is summarized in Figure 8.4.
Region 1
Region 2
Region 3
No service K=0
Full
Fullservice
serviceK=1
K=1
Centralized channel
(D K ) 2
f
4E
T
T
(D K ) 2
f
4E
D2
4E
T
No service K=0
Full service K=1
Full service K=1
Profit sharing
T
ff
(D K ) 2
f
4E
T
D2
4E
ff
No service K=0
Full service K=1
Full service K=1
f
Decentralized channel
T
3(D K ) 2
f
16E
T
K (K 2D )
16 E
3D 2
16E
K (K 2D )
4E
Figure 8.4: Performance of the centralized channel, profit sharing and decentralized
channel
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CHAPTER
8
From Figure 8.4 it can be seen that the profit sharing mechanism provides full service in
and
2
(i.e.,
when f d
K (K 2D )
).
4E
Regions
1
(when f t
K (K 2D )
), both the profit sharing mechanism and the centralized channel
4E
However,
in
Region
3
provide no service. Since the SC profit under the profit sharing scenario is same as the
profit of the centralized scenario in all three regions, it can be concluded that any profit
sharing mechanism [0,į3] coordinates the SC for all values of f.
(ii) To prove the second part of the theorem it remains to be shown that win-win
opportunities are achieved in all three regions of Figure 8.3.
Region 1: The Buyer’s profit under the decentralized scenario in Region 1 is
§ (D K ) 2
·
¨¨
f ¸¸ . Therefore profit sharing provides a higher profit to the Buyer in Region
© 16 E
¹
1 as compared to the decentralized scenario iff:
§ (D K ) 2
·
¸ : G 3 .
2
4 ¨© (D K ) 4 fE ¸¹
3
G3 ¨
(8.54)
§ (D K ) 2 ·
¸ . So, profit
The Supplier’s profit in the decentralized situation in Region 1 is ¨
¨ 8E
¸
©
¹
sharing provides a higher profit to the Supplier in Region (1) compared to the
decentralized situation iff:
§ (D K ) 2
·
¸ : G 3 .
2
2 ¨© (D K ) 4 fE ¸¹
1
G3 ! ¨
(8.55)
It follows that win-win can be achieved in Region 1 since:
G 3 G 3
Inside_proefschrift_Vijayender_06.indd 200
(D K ) 2
(D K ) 2 4Ef
! 0.
(8.56)
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201
Equation (8.56) will always be greater than zero since the parameters D and K are
positive values. This implies that profit sharing provides win-win in Region 1 when
·
·
1 § (D K ) 2
3 § (D K ) 2
¨¨
¸
¨¨
¸.
G
3
2
2
¸
2 © (D K ) 4 fE ¹
4 © (D K ) 4 fE ¸¹
§ D2 ·
¸¸ .
Region 2: The Buyer’s profit in the decentralized situation in Region 2 is ¨¨
© 16 E ¹
Therefore profit sharing provides a higher profit to the Buyer in Region 2 when compared
to the decentralized scenario iff:
1§
D2
4 © (D K ) 2 4Ef
·
¸¸ : (G 3 ) .
¹
G 3 1 ¨¨
(8.57)
§D 2 ·
¸¸ . It can be
The Supplier’s profit in the decentralized scenario in Region 2 is ¨¨
© 8E ¹
concluded that profit sharing provides a higher profit to the Supplier in Region 2 when
compared to the decentralized scenario iff:
1§
D2
G 3 ! ¨¨
2 © (D K ) 2 4Ef
·
¸¸
¹
(G 3 ) .
(8.58)
It can be concluded that a win-win opportunity is achieved in Region 2 since:
(G 3 ) (G 3 ) Summarizing,
win-win
1§
D2
¨¨
2 © (D K ) 2 4Ef
D2
3§
1 ¨¨
4 © (D K ) 2 4Ef
opportunities
are
·
1§
D2
¸¸ G 3 1 ¨¨
4 © (D K ) 2 4Ef
¹
·
¸¸ ! 0 .
¹
achieved
(8.59)
in
Region
2
when
·
¸¸ .
¹
§ D2 ·
¸¸ .
Region 3: The Buyer’s profit under the decentralized scenario in Region 3 is ¨¨
© 16 E ¹
Profit sharing provides a higher profit to the Buyer in Region 3 when compared to the
decentralized situation iff: G 4 34 . Furthermore, the Supplier’s profit in the decentralized
§D 2 ·
¸¸ , so that profit sharing provides a higher profit to
situation in Region 3 is given by ¨¨
© 8E ¹
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8
the Supplier in Region 3 when compared to the decentralized situation iff: G 3 ! 12 . It can
be concluded that win-win is achieved in Region 3 when 12 G 3 34 .
Summarizing, the results for the three regions, we can conclude that the profit sharing
mechanism [0,į3] provides win-win opportunities with respect to the decentralized
(solitaire) scenario in all three regions.Ŷ
Example (continued)
In the numerical examples, by assuming that G 3
3
5
it can be seen that the profit sharing
mechanism coordinates the service-level decision when f d 550 . In Example [1], since
f
200 (which lies in Region 2), the Buyer will provide full service. The profits for the
Buyer, Supplier and the SC can be obtained as 640, 960 and 1600, respectively. In
Example [2], since f
300 (also in Region 2), the Buyer will provide full service. The
profits for the Buyer, Supplier and the SC can be obtained as 600, 900 and 1500,
respectively. For Example [3], f
600 (which lies in Region 3), so the Buyer will
provide no service. The profits for the Buyer, Supplier and the SC can be obtained as 500,
750 and 1250, respectively. Note that in all three examples the SC profit is equal to that
in the centralized scenario (i.e., the SC is coordinated) and that also in all three examples
both the Buyer and the Supplier have a higher profit when compared to the solitaire
scenario (i.e., win-win is achieved).Ŷ
8.7
Quantity discount mechanism
With the quantity discount mechanism (denoted by a subscript 4), the Supplier fixes a
base price W 4 and charges an additional price which is a decreasing function in Q4 . At its
simplest form, the price at which the Supplier sells the product to the Buyer is dependent
upon the order quantity as given by:
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W4 (Q4 ) W 4 P4
Q4
.
203
(8.60)
The profits for the Buyer, Supplier and the SC with the quantity discount mechanism can
be obtained as:
( P4 W 4 )Q4 P 4 K 4 f ;
B4 (Q4 , K 4 )
S 4 (Q4 , K 4 ) W 4 Q4 P 4 ; and
T4 (Q4 , K 4 )
respectively, where Q4
P4 Q4 K 4 f
(8.61)
(8.62)
(8.63)
D E P4 KK 4 .
The following theorem summarizes the potential of the quantity discount mechanism to
provide coordination and win-win opportunities.
Theorem 8.4
For all f there is a quantity discount contract [W 4* , P 4 ] such that
(i)
the SC is coordinated;
(ii)
win-win opportunities are achieved.
Proof
(i) Evidently, the Buyer will choose the order size that optimizes his profit. The Buyer’s
optimal quantity Q4 can be obtained from Equation (8.61) as:
Q4
1
2
D KK
4
W 4 E .
(8.64)
Recall that the optimal order size from the centralized scenario is given by:
Q0*
1
2
D KK1 .
(8.65)
From Equations (8.64) and (8.65) it is clear that the Buyer’s optimal order size is also the
SC optimal order size when W 4 = 0. We will therefore consider a quantity discount
contract [W 4* , P 4 ] where W 4*
0 . Under such a contract, the profits for the Buyer, Supplier
and SC are given by:
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CHAPTER
§ (D KK 4 ) 2 ·
¸¸ P 4 K 4 f ;
B4 ( P 4 , K 4 ) ¨¨
4E
©
¹
S 4 (P 4 )
(8.66)
P 4 ; and
(8.67)
§ (D KK 4 ) 2 ·
¨¨
¸¸ K 4 f .
4E
©
¹
T4
8
(8.68)
The Buyer’s profit when he provides no service with the quantity discount contract can
be obtained as:
§D2 ·
¸¸ P 4 .
B4 ( P 4 ,0) ¨¨
© 4E ¹
(8.69)
Similarly, the Buyer’s profit when he provides full service with the quantity discount is:
§ (D K ) 2 ·
¸¸ P 4 f .
B4 ( P 4 ,1) ¨¨
© 4E ¹
(8.70)
It follows that the Buyer will provide full service when:
f d
K (K 2D )
.
4E
(8.71)
In conclusion, the following holds:
If f d
K (K 2D )
,
4E
then K
B4
if f !
K (K 2D )
,
4E
(D K ) 2
P4 f ; S4
4E
then K
B4
D K
; Q4*
2E
1 and P4*
0 ; P4*
D2
P4 ; S4
4E
D
2E
; Q4*
P 4 ; T4
D K
P 4 ; T4
2
(D K ) 2
f ; and
4E
D
2
D2
.
4E
In other words, Equation (8.71) illustrates that the region for service coordination is same
as that in the centralized scenario. The quantity discount contract coordinates both the
pricing and service-level decisions for all values of the cost of service provision. The
performance of the quantity discount mechanism is summarized in Figure 8.5.
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Region 1
Region 2
Region 3
No service K=0
Full
Fullservice
serviceK=1
K=1
Centralized channel
(D K ) 2
f
4E
T
205
T
(D K ) 2
f
4E
D2
4E
T
ff
No service K=0
Full service K=1
Full service K=1
ff
Quantity
Quantitydiscount
discount
T
(D K ) 2
f
4E
T
D2
4E
No service K=0
Full service K=1
Full service K=1
f
Decentralized channel
T
3(D K ) 2
f
16E
T
K (K 2D )
16 E
3D 2
16E
K (K 2D )
4E
Figure 8.5: Performance of the centralized channel, quantity discount and decentralized
channel
From Figure 8.5 it can be seen that the quantity discount mechanism provides full service
in Regions 1 and 2 (i.e., when f d
(when f t
K (K 2D )
). However, in Region 3
4E
K (K 2D )
), both the quantity discount mechanism and the centralized channel
4E
provide no service. Since the SC profits with the quantity discount mechanism are the
same as the profits of the centralized scenario in all three regions, it can be concluded that
any quantity discount contract [0, P4 ] coordinates the SC for all values of f.
(ii) It remains to be shown that win-win opportunities are achieved in all three regions in
Figure 8.5.
Region 1: The Buyer’s profit in the decentralized situation in Region 1 is
§ (D K ) 2
·
¨
f ¸ . The quantity discount contract thus provides a higher profit to the
¨ 16E
¸
©
¹
Buyer in Region 1 when compared to the solitaire scenario iff:
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CHAPTER
P4 3(D K ) 2
16E
: P4 .
8
(8.72)
§ (D K ) 2 ·
¸¸ . The
Similarly, the Supplier’s profit in decentralized situation in Region 1 is ¨¨
© 8E ¹
quantity discount provides a higher profit to the Supplier in Region 1 when:
P4 !
(D K ) 2
: P4 .
8E
(8.73)
Win-win is achieved in Region 1 because P 4 P4
(D K ) 2
! 0.
16E
It
can
is
when
(D K ) 2
3(D K ) 2
P4 .
8E
16E
be
concluded
that
win-win
achieved
in
Region
1
Region 2: The Buyer’s profit in the decentralized situation in Region 2 is given by
§ D2
¨¨
© 16 E
·
¸¸ . It follows that the quantity discount contract provides a higher profit to the
¹
Buyer in Region 2 when compared to the solitaire scenario iff:
P4 4(D K ) 2 D 2 16Ef
16E
: ( P4 ) .
(8.74)
§D 2 ·
¸¸ .
Furthermore, the Supplier’s profit in the decentralized situation in Region 2 is ¨¨
© 8E ¹
The quantity discount contract provides a higher profit to the Buyer in Region 2 when
compared to the decentralized scenario iff:
P4 !
2D 2
: (P 4 ) .
16 E
(8.75)
Win-win is achieved in Region 2 because:
(P4 ) (P4 )
4(D K ) 2 3D 2
f ! 0.
16 E
(8.76)
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The condition in Equation (8.76) is true since f 207
4K (K 2D ) D 2
in Region 2. The
16E
conclusion is that win-win is achieved in Region 2 when:
2D 2
4(D K ) 2 D 2 16Ef
P4 .
16E
16E
Region 3: The Buyer’s profit in the decentralized situation in Region 3 is given by
§ D2
¨¨
© 16 E
·
¸¸ . The quantity discount contract provides a higher profit to the Buyer in Region
¹
(3) when compared to the decentralized case iff:
P4 3D 2
: P4 .
16E
(8.77)
§D 2 ·
¸¸ . Hence,
The Supplier’s profit in the decentralized scenario for Region 3 is equal to ¨¨
© 8E ¹
the quantity discount contract provides a higher profit to the Buyer in Region 3 when
compared to the solitaire scenario iff:
P4 !
Clearly, P 4 P 4
Region 3 when
D2
8E
P4 .
(8.78)
D2
! 0 . Hence it can be concluded that win-win is achieved in
16 E
D2
3D 2
P4 .
8E
16E
Summarizing, the quantity discount mechanism [0;μ4] provides win-win opportunities in
all three regions.Ŷ
Example (continued)
By assuming that P 4
800 , it can be seen that the profit sharing mechanism coordinates
the service-level decision in the numerical examples when f d 550 .
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8
200 (which lies in Region 2), the Buyer will provide full
In Example [1], since f
service. The profits for the Buyer, Supplier and the SC can be obtained as 800, 800 and
1600, respectively.
In Example [2], since f
300 (also in Region 2), the Buyer will provide full service.
The profits for the Buyer, Supplier and the SC can be obtained as 700, 800 and 1500,
respectively.
For Example [3], f
600 (which lies in Region 3), so the Buyer will provide no service.
The profits for the Buyer, Supplier and the SC can be obtained as 450, 800 and 1250,
respectively. Note that in all three examples the SC profit is equal to that in the
centralized scenario (i.e., the SC is coordinated) and that also in all three examples both
the Buyer and the Supplier have higher profits when compared to the solitaire scenario
(i.e., win-win is achieved).Ŷ
8.8
License fee mechanism
The so-called two-part tariff or license fee contract is governed by the parameters
W5 and L5 , where W5 is the wholesale price and L5 is a fixed license fee (i.e., an amount
for carrying the product which is not dependant on the quantity ordered) paid by the
Buyer to the Supplier. It is easy to see that when P 4
L5 and W 4*
W5* , the license fee
contract [ W5* , L5 ] has exactly the same effect as the quantity discounts contract [W 4* , P 4 ]
which leaves us with the following result.
Corollary 8.5
For all f there is a license fee contract [W5* , L5 ] such that
(i)
the SC is coordinated
(ii)
win-win opportunities are achieved.
Example (continued)
The results for the numerical example are summarized in Table 8.1.
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Example 1
Scenario
B
Centralized
0;J
Profit Sharing [ W
0;G
Quantity discount [ W
License fee [ W
0; P
0; L
T
B
S
T
B
S
T
-
-
1600
-
-
1500
-
-
1250
625
937
312
625
937
312
625
937
700
900
1600
469
789
1250
469
781
1250
]
640
960
1600
600
900
1500
500
750
1250
800 ]
800
800
1600
700
800
1500
450
800
1250
800
800
1600
700
800
1500
450
800
1250
5
8
3
5
S
Example 3
312
Solitaire
Revenue Sharing [ W
Example 2
209
800 ]
]
Table 8.1: Numerical examples results summary when the Buyer provides service
From the summary of the numerical examples it is clear that the Buyer provides no
service for all the three numerical examples. The SC profit in the decentralized scenario
is lower than the centralized scenario for all the three cases. With the revenue sharing
mechanism the service-level decision is not coordinated for the numerical Example [2].
The profit sharing, quantity discount and the license fee mechanism coordinates both the
price and the service-level decisions for all the three examples.Ŷ
In the next section, we analyze a situation in which the Supplier decides and provides the
level of service provided to the end-consumer.
8.9
Model where the Supplier decides the service provision
The model considered in this section resembles the earlier model with one exception;
here we assume that the Supplier and not the Buyer decides the service-level provided.
For completeness we introduce the full model below.
Consider the situation in which the Supplier offers a quantity of products Q to the Buyer
at a price of W per unit. It is also assumed that the Buyer and the Supplier have full
information as to the demand function and the costs incurred by each player.
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8
Furthermore, it is assumed that the final customer demand D for the product depends both
on the price P set by the Buyer and on the service-level K provided at the Buyer’s outlet.
The service-level is normalized such that 0 d K d 1 . In it simplest form, the end-consumer
demand linearly decreases with price and increases with the level of service provided at
the Buyer’s outlet, i.e.,
D ( P , K ) D E P KK ,
(8.79)
with D, E, Ș > 0. Clearly, K is a parameter that represents the maximum level up to which
the demand can be increased by improving the service-level. The service provision comes
at a cost (represented by f) and this cost of service provision is proportional to the level of
service provided. As mentioned, the only difference in this setting is that the Supplier
decides on the service-level K and also incurs the cost of service provision. The Buyer
decides on the final selling price and order quantity based on the wholesale price and the
service-level provided by the Supplier. The SC described above is depicted in Figure 8.6.
Supplier
Supplier
(Decide: W,K)
(Decides :W,K)
Q
W
Q
W
Q
Q
Buyer
Buyer
(Decide: P),
(Decides : P)
.
Κ
P
Customer
Customer
P
KK
D
D(( P
P)) = αD −βEPP+η K
Figure 8.6: SC setting when the Supplier provides the service-level
Clearly, the result in the centralized scenario remains valid. In the next subsection we
present the results of the solitaire scenario.
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8.9.1
211
Solitaire Scenario analysis
The profits for the Buyer, Supplier and the SC under the solitaire scenario (denoted by
subscript 6) can be obtained as:
B6
S6
T6
(D EP6 KK 6 )( P6 W6 ) ;
(8.80)
(D EP6 KK 6 )W6 K 6 f ; and
(8.81)
(D EP6 KK 6 ) P6 K 6 f
(8.82)
Respectively, where K 6 is the service-level provided, which is the Supplier’s decision
variable in this setting.
The following theorem summarizes the main results of the analysis of the solitaire
scenario.
Theorem 8.6
(i)
In a decentralized SC, the Buyer fixes the final price at a higher level and orders
lower quantities when compared to the centralized SC. As a result, this leads to a
lower profit for the entire SC.
(ii)
If
K (K 2D )
K (K 2D )
d f d
, then the Supplier in a decentralized SC will
8E
4E
choose to provide no service whereas the centralized channel will provide full
service.
The proof of this analysis follows along the same lines as the case in which the Buyer
provides the service-level and is therefore omitted here.
It can be seen from Theorem 8.6 that the uncoordinated region is somewhat smaller for
this case when compared to the case in which the Buyer decides the service-level.
Intuitively, the reason for such a behavior can be attributed to the fact that the Supplier
can recover some of the service costs in the wholesale price he charges to his Buyer.
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However, the Buyer does not have this privilege when he incurs the service costs and
hence provides a lower service.
Example (continued)
The Supplier in a decentralized channel will provide full service when f d 275 .
In Example [1], f = 200 < 275 so that the unique optimal solution is P6*
K 6* 1 with SC profit T6
1100 T0
37.5 and
1600 . The profits for the Buyer and Supplier can
be obtained as 400 and 700, respectively.
For Example [2], f = 300 > 275 with the unique optimal solution of P6*
K 6*
0 and SC profit T6
937.5 T0
unique optimal solution of P6*
37.5 and
1500 . In Example [3], f = 600 > 275 giving the
37.5 and K 6*
0 with SC profit T6
937.5 T0
1250 .
For Examples [2] and [3], the profit for the Buyer is 312.5 and that of the Supplier is 625.
Moreover, in all three examples the SC profit in the decentralized channel is lower than
that in the centralized channel.Ŷ
8.9.2
Contract Mechanisms
The following theorem summarizes the results for the various coordinating mechanisms
in case the service-level is determined by the Supplier.
Theorem 8.6
(i)
Revenue sharing:
(a) There is a revenue sharing contract [W7* , J 7 ] such that the SC is coordinated if
and only if f d J 7
K (K 2D )
K (K 2D )
or f t
.
4E
4E
(b) For all f there is a revenue sharing contract [W7* , J 7 ] such that win-win
opportunities are achieved.
(ii)
Profit sharing
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213
For all f there is a profit sharing contract [W8* , G 8 ] such that
(a) the SC is coordinated
(b) win-win opportunities are achieved.
(iii) Quantity discount
For all f there is a quantity discount [W 9* , P 9 ] such that
(a) the SC is coordinated
(b) win-win opportunities are achieved.
(iv) License fee
For all f there is a license fee [W10* , L10 ] such that
(a) the SC is coordinated
(b) win-win opportunities are achieved.
The proof of the above theorem is omitted here since it follows along the same lines as
that for the revenue sharing mechanism when the Buyer decides the service-level.
It is immediately clear from Theorem 8.6 that the results are similar to the case where the
service-level was determined by the Buyer.
Example (continued)
The results for the numerical example are summarized in Table 8.2.
Example 1
Scenario
B
Centralized
0;J
Profit Sharing [ W
0;G
Quantity discount [ W
License fee [W
0; P
0; L
T
B
S
T
B
S
T
-
-
1600
-
-
1500
-
-
1250
700
1100
312
625
937
312
625
937
900
700
1600
625
625
1250
469
781
1250
]
740
880
1600
720
780
1500
500
750
1250
925 ]
875
725
1600
875
625
1500
325
925
1250
875
725
1600
875
625
1500
325
925
1250
1
2
3
5
S
Example 3
400
Solitaire
Revenue Sharing [ W
Example 2
925 ]
]
Table 8.2: Numerical examples results summary when the Supplier provides service
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8
From the Table 8.2 it is clear that in the decentralized channel the Supplier provides full
service for the numerical Example [1], and provides no service for the Example [2] and
Example [3]. Whereas, when the Buyer provides service the decentralized channel does
not provide any service for all the three numerical examples. The SC profit in the
decentralized scenario is lower than the centralized scenario for all the 3 cases. With the
revenue sharing mechanism, the service-level decision is not coordinated for the
numerical Example [2] as in the case when the Buyer provides full service. For both the
cases the profit sharing, quantity discount and the license fee mechanism coordinates both
the price and the service-level decisions and provides win-win for all the three
examples.Ŷ
8.10 Conclusions
In this chapter, it is shown that when the end-consumer demand is a function of both the
price and service-level, a decentralized SC fails to coordinate both the price and servicelevel decisions. Four contract mechanisms for overcoming such difficulty are reviewed. It
has been observed that revenue sharing coordinates the pricing decision but not the
service-level decision for all the values of the cost of service provision. However,
revenue sharing does provide win-win opportunities for the entire range of the cost of
service provision. The profit sharing, quantity discounts and license fee mechanisms do
coordinate the pricing and service-level decisions and also provide a win-win solution for
the entire range of the cost of service provision. It has also been shown that in the
decentralized channel the Supplier provides full service for a greater range of the
parameter values when compared to the situation where the Buyer decides on the servicelevel. Intuitively, the reason for such a behavior can be attributed to the fact that the
Supplier can recover some of the service costs in the wholesale price he charges to his
Buyer. However, the Buyer does not have this privilege when he incurs the service costs
and hence provides a lower service. Also, performance of the contract mechanisms is
more-or-less the same for both the cases, namely the Buyer decides about the servicelevel and the Supplier decides about the service-level. From a managerial point of view in
214
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215
all feasible situations it is always better for the Supplier to take up the service provision
and also use one of the three (profit sharing, license fee and quantity discounts) contract
mechanisms.
This study offers many possibilities for further research. One good extension would be to
study the coordination of pricing and service decisions by introducing information
asymmetry, i.e., only the Buyer knows the effect of service on the end-consumer demand
with certainty. Other possible extensions include lengthening the SC, introducing
competition at Buyer and/or Supplier level, and considering different demand functions.
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
217
Part 4: Contract Mechanisms for Coordinating Product
line Decisions in a Supply Chain
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9
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
219
Chapter 9
Using Contract Mechanisms to Coordinate Product line Decisions 9
Chapter Synopsis
This chapter addresses product line decisions in a Supply Chain (SC) with a Buyer and a
Supplier. The end-consumers are comprised of two segments with a different willingnessto-pay. The final demand and the segments’ willingness-to-pay are assumed to be
deterministic. In this setting, it is demonstrated that if the decisions are decentralized, the
SC can either stocks the same, a lower, or a higher number of product variants when
compared to a centralized SC. It is also shown that under certain conditions the
decentralized SC can have a wrong focus, i.e., sells a single product to only the segment
with a high willingness-to-pay, when a centralized SC would sell a single product to both
the segments. In fact the decision of the decentralized SC to stock less, more, or to have a
wrong focus, when compared to the centralized SC, depends on the willingness-to-pay of
different segments, segment size, and the costs associated with producing different
variants. In all cases where the decentralized SC behaves differently than the centralized
SC, the overall SC performance is sub-optimal. To overcome this issue, various contract
mechanisms are reviewed and checked for their ability to achieve maximum SC profit
(SC is coordinated) and to provide both the Supplier and the Buyer with higher profits
when compared to the decentralized scenario (win-win). It is shown that the frequently
used slotting allowance mechanism can coordinate and provide win-win opportunities in
a region where the decentralized SC stocks less than the optimal number of product
variants. However, it is also demonstrated that the slotting allowance mechanism fails to
coordinate the SC in a situation where the decentralized SC stocks a higher than optimal
number of product variants or when the decentralized SC has a wrong focus. However, it
is demonstrated that both the revenue and profit sharing mechanisms provide
9
This chapter is the reengineered version of the paper presented at the 22nd EURO conference in Prague in
July 2007. [Reference: Nalla, V. R, J.A.A van der Veen, and V. Venugopal (2007)].
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coordination and win-win opportunities under all possible parameter values. Moreover,
an equivalence relationship is established between the revenue and profit sharing
mechanism.
9.1
Introduction
Consider the case of Hewlett Packard (HP), the world’s largest manufacturer of DeskJet
printers. The end-consumers who want to buy a DeskJet printer and who walk into a
retail market such as Media Markt (Europe’s largest retailer for consumer electronics)
will have a different willingness-to-pay based upon their usage and preference for that
particular product. By understanding the consumer’s price sensitivity, HP can decide to
launch different printer models (with various features and aesthetic appeal) in order to
cater to different market segments and extract all potential revenue from consumer
segments. However, it is Media Markt who makes the final decision on the number of
variants to be stocked in their stores and the price of each of the variants. Clearly, Media
Markt is aiming to maximize its own profits. Given this fact, it is not unlikely that an
electronic devices retailer typically stocks less or more of a variant than what is optimal
for the SC as a whole. In this chapter, we suggest mechanisms which can enable
coordination (together the Supplier and the Buyer will optimize the SC) and win-win
opportunities (Supplier and Buyer) when the Buyer stocks a non-optimal number of
variants.
The marketing literature suggests slotting allowances as a mechanism to increase the
efficiency of the product line decisions, see e.g., Desiraju (2001), Shafer (2005), and
Sudhir & Vitala (2006). Slotting allowances are lump-sum payments made by the
manufacturer to the retailers for stocking new variants. However, the literature on slotting
allowance does not address the issue of coordination by comparing the performance of
the centralized and the decentralized SC. More importantly, it does not address the issue
of win-win opportunities (benefit for all the players in a SC).
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221
In this chapter, we address the product line decisions in a SC with a focus on coordination
and win-win opportunities. A two stage SC with a Buyer and a Supplier is considered.
The end-consumers are comprised of two different consumer segments that have a
different willingness-to-pay. In this setting, it is demonstrated that if the decisions are
decentralized (i.e., the Supplier and Buyer both optimize their own situation), the SC
results are sub-optimal when compared to a centralized SC. This is witnessed by the fact
that the decentralized SC offers a lower or a higher number of product variants when
compared to a centralized SC or where it has a “wrong focus” whereby it sells a single
product to the high willingness-to-pay segment when a centralized SC would sell a single
product to both the segments.
It is the objective of this chapter to study whether various contract mechanisms
(agreements between the Supplier and Buyer on various contract parameters) can
overcome the difference in performance between the centralized and decentralized SC.
More specifically, the contract mechanisms are evaluated on their ability to provide
coordination (optimal SC performance is achieved) and win-win (both the Supplier and
Buyer achieve better performance when compared to the decentralized SC).
It is shown that the frequently used slotting allowance mechanism can coordinate and
provide a win-win opportunity in a region where the decentralized SC stocks less than the
optimal number of product variants. However, it is also demonstrated that the slotting
allowance mechanism fails to coordinate the SC in a situation where the decentralized SC
stocks a higher than optimal number of product variants or when the decentralized SC has
a wrong focus.
To find the type of contract that repairs all mismatches between the centralized and
decentralized SC, the revenue and profit sharing mechanisms are designed. It will be
shown that indeed coordination and win-win opportunities are achieved for all possible
parameter settings. Moreover, an equivalence relationship is established between the
revenue and profit sharing mechanisms.
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There are two main bodies of literature related to this chapter: the literature on conflict
and coordination in a SC and the literature on product-line design. In relation to the
former, this chapter can be seen as identifying a new form of coordination problem in a
SC, namely the lack of coordination on the product-line being supplied. This effect seems
to be particularly important given that most manufacturers sell a product-line (several
variants) rather than a single product.
There is also extensive literature on product-line design with a seller facing different
consumer segments, see e.g., Mussa & Rosen (1978); Moorthy (1984); Oren, Smith, &
Wilson (1984); Reibstein & Gatignon (1984); Shugan (1984); Dolan (1987); Gerstner &
Hess (1987); Dobson & Kalish (1988); Balachander & Srinivasan (1994) and Zenor
(1994). This chapter largely follows the setting in Villas-Boas (1998). However, the
consideration and treatment of the problem are very different from that paper. Our study
contributes insights to the coordination literature and adds to the knowledge of
coordinating product line decisions within a SC.
The reminder of the chapter is organized as follows. In the next section, the basic model
is introduced and analyzed for the centralized and the decentralized SC. In Section 3, we
first suggest the slotting allowance as a mechanism to coordinate and provide a win-win
opportunity in a region where the decentralized SC stocks less than the optimal number
of product variants. Subsequently, we design the revenue and profit sharing mechanisms.
The final section deals with the conclusions and directions for further study.
9.2
Model and basic analysis
Consider a setting in which two different consumer segments have different willingnessto-pay: high willingness-to-pay consumers (Highs for short) and low willingness-to-pay
consumers (Lows). The high segment size is denoted by D and the low segment size is (1D) so that the total market size is normalized to unity. Both consumer segments require a
product which fulfills certain functional requirements. It is assumed that the same product
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223
cannot be sold at two different prices to different segments. Note that this assumption
does not hold for all markets; in fact revenue management is frequently used, and
basically revenue management is all about separating markets and selling the same
product to different consumer segments at different prices.
The product supplier can target two different variants with similar functional
requirements to different consumer segments. In such a situation, it is assumed that the
product targeted to the Highs has additional features (with respect to the aesthetic appeal
and other features). The Supplier incurs higher production costs (denoted by ch) to
provide additional features for the high-end product. The Supplier might be interested in
offering a higher-end product at a higher production cost because he considers this as a
strategy to extract the surplus from both consumer segments. The Supplier will be
interested in such a strategy as long as the surplus he can extract from the high-end
segment exceeds the additional costs he will incur in providing additional features. As it
does not fundamentally influence the analysis, the cost of producing a basic product is
normalized to zero for simplicity. Furthermore, it is assumed that all consumers have
already decided to purchase a product manufactured by the Supplier so that the effects of
competition have no influence in our model. Other assumptions are that there is
information symmetry among all the players in a SC, and the willingness-to-pay of the
consumers for a given product type is given (i.e., is exogenous) and fixed. The Supplier
makes a decision on the wholesale prices for the two variants that he wants to offer and
the Buyer will decide which of these variants to stock and which consumer segments to
target. More precisely, the SC decisions will result in one of the following three options:
1)
Sell a basic product to the Highs only;
2)
Sell a basic product to both the segments; or
3)
Sell different variants to different consumer segments (basic product to Lows and
featured product to Highs).
Note that each option has its pros and cons. Option 1 has a smaller target market, but the
price charged can be higher when compared to Option 2. At Option 3 each target market
can be reached at its willingness-to-pay but the per-unit manufacturing costs are higher
when compared to Options 1 and 2.
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9
The willingness-to-pay of the Highs and Lows is denoted by ph and pl , respectively. The
Supplier fixes the wholesale price of the basic product at Wl and the wholesale price for
the product with more features at Wh . The Buyer decides the variants that need to be
stocked and decides the consumer price based on the Supplier’s wholesale price decision
for each of the variants. Both the Supplier and the Buyer intend to maximize their firms’
profit and are less concerned about the whole SC. The pictorial representation of this SC
is given in Figure 9.1.
ph
ph
Wl
Supplier
Supplier
Wh
High consumer segment D
()
High consumer segment ( α )
Wl
Buyer
Wh
Buyer
Low consumer segment (1 -D )
pl
Low consumer segment (1- α )
pl
Figure 9.1: A two-stage supply chain with two consumer segments
In the next sub-section, we analyze the centralized scenario.
9.3
Centralized Scenario analysis
First consider the centralized scenario, i.e., the situation in which the Supplier and the
Buyer operate as a single unit and work jointly to optimize SC profit. As mentioned, a
centralized SC has the following three options:
A) Sell a single product to the Highs only. With this option the consumer price is set at
ph and the generated profit is given by Dp h ;
B) Sell a single product to both segments. With this option the price is set at pl and the
generated profit is given by pl ;
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
225
C) Produce two different variants of the product and sell each product to the associated
segment. With this alternative the prices are set at pl and ph, respectively and the SC
profit is given by D ( p h c h ) (1 D ) pl .
It follows that Option A is better than (generates a higher or equal SC profit than) Option
B iff pl d Dph ; Option C is better than Option B iff pl d p h ch ; and Option C is better
than Option A iff pl t
D
ch .
1D
Throughout this chapter, it is assumed that:
(1 D ) p h t ch .
(9.1)
The reason for this assumption is that if it is violated, the option to stock two products
(Option C) can never be optimal (the cost of producing the featured product is too high)
and thereby our study on product line decisions would become irrelevant. Under
Assumption (9.1), it is easy to see that
D
1D
c h d Dp h d p h c h .
(9.2)
It follows that Option A is preferred over the other two options iff pl d Dp h ; Option C is
the best of the three options when:
D
c h d pl d p h c h
1D
(9.3)
and Option B gives the highest SC profit if pl t ph ch (note that if an equality holds,
two options result in the same SC profit). The results on the performance of the
centralized SC are depicted in the Figure 9.2.
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CHAPTER
Option A best
Option A best
Option C second best
Option C second best
Centralized channel
Centralized channel
Option C best
Option C best
Option C best
Option C best
Option A second best
Option B second best
Option A second best
Option B second best
Option B worst
Option B worst
Option B worst
Option B worst
D
D
1 cDh
1D
Option A worst
Option A worst
Option A worst
Option A worst
Two products
Two products
Single product to Highs
Single product to Highs
CH
Dph DPH
Option B best
Option B best
Option C second best
Option C second best
pl pl
9
PL
Single product to all
Single product to all
P CH
ph chH
Figure 9.2: Centralized SC performance
In the next sub-section we analyze the solitaire scenario (decentralized SC).
9.4
Solitaire scenario
In the decentralized scenario, also called solitaire scenario and denoted by subscript 1,
both the Buyer and Supplier maximize their own profits. The Supplier can sell two
variants to the Buyer. Knowing the wholesale prices, the Buyer will decide among the
three possible options discussed earlier with the objective to maximize his own profits.
Since we assume symmetric information between the Supplier and the Buyer, the
Supplier can anticipate the behavior of the Buyer to determine the two different
wholesale prices for the two variants. This also implies that the Supplier will produce and
sell two variants only if the Buyer will decide to stock the two variants.
Assume that the Supplier offers two products at wholesale prices Wl1 and Wh1 ,
respectively. Similar to the earlier analysis, the Buyer then faces the following three
options:
Option 1:
Sell the basic product to Highs at price ph . In that case his profit is given by:
B1
Option 2:
D ( p h Wl ) .
1
Sell a single product to both the segments at price pl, in which case the
Buyer’s profit is equal to: B1
pl Wl1 .
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
Option 3 :
Sell two different products to different segments. Here the profit for the
Buyer is described by: B1
D ( ph Wh ) (1 D )( pl Wl ) .
1
1
Turning to the Supplier, it can be observed that he also has 3 options:
Option A:
Offer a single product targeted at the Highs. Clearly, under this option, the
Supplier would set the wholesale price optimally at Wl1
p h . This results in
the following profits for the Supplier, Buyer, and SC:
S1
Option B:
Dph ; B1 = 0; and T1
Dp h .
S1 B1
(9.4)
Offer a single product, targeted to both the segments. Under this option, the
Supplier wants to set a price Wl1 such that his own profit is maximized, but
he also has to ensure that the Buyer prefers Option 2 over Option 1. In other
words, the Supplier is solving the following problem:
^
`
Max Wl1 ( pl Wl1 ) t D ( p h Wl1 ) .
(9.5)
It is easy to see that this problem is solved by Wl1
p l Dp h
.
1D
It follows that the profits of Supplier, Buyer and SC are given by:
S1
Option C :
p l Dp h
; B1
1D
D ( p h pl )
; and T1
1D
S1 B1
pl .
(9.6)
Offer two products at wholesale prices Wl1 and Wh1 ,respectively. Obviously,
here the Supplier wants to determine the two wholesale prices such that his
profit is maximized, while ensuring that the Buyer indeed does adopt both
products. This problem can be formulated as the following linear
programming problem:
^
`
Max D (Wh1 c h ) (1 D )(Wl1 )
(9.7)
D ( p h Wh ) (1 D )( pl Wl ) t D ( ph Wl )
1
ST
1
1
D ( p h Wh ) (1 D )( pl Wl ) t ( pl Wl )
1
1
1
Wh1 t Wl1
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9
Note that the two first constraints ensure that the Buyer prefers Option 3
over the other two options.
Lemma 9.1
The linear programming problem (9.7) is solved by Wh1
Wl1
pl .
Proof
The LP problem (9.7) can be re-written as:
^
Max DWh1 (1 D )Wl1 Dch
pl t
`
Į
( 1 2Į)
Wh Wl
( 1 Į) 1 ( 1 Į) 1
pl t p h Wl1 Wh1
ST
(i)
(ii)
Wl1 d Wh1
(iii)
The intersection of constraints (i) and (ii) is given by:
Wl1
§ 1 ·
§ D ·
¨
¸ pl ¨
¸ ph ; Wh1
©1D ¹
©1D ¹
§ 1 ·
§ 1 2D ·
¨
¸ pl ¨
¸ ph .
© 1D ¹
©1D ¹
It is easy to verify that this in fact is an extreme point. The profit at this extreme point is
given by:
S1
§ D 2 ·
§ D 2 1D ·
¨¨
¸¸ p h ¨¨
¸¸ pl Dch .
©1D ¹
© 1D ¹
(9.8)
The intersection of constraints (i) and (iii) leads to the following wholesale prices:
Wl1
pl ; Wh1
pl . Again, it is easy to verify that the above wholesale prices form
another extreme point. The Supplier’s profit in this extreme point is given by:
S1
p l Dc h .
(9.9)
It is easy to see that the constraints (ii) and (iii) form two parallel lines which do not
intersect and hence do not lead to an extreme point.
It can therefore be concluded that the LP problem (9.7) has only two extreme points.
Clearly, the optimal solution will be the extreme point with the highest profit. Note that:
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
§§ D 2 ·
·
§ D 2 1D ·
¸¸ pl Dch ¸
¸¸p h ¨¨
( pl Dch ) ¨¨ ¨¨
¸
© 1D ¹
©©1D ¹
¹
§ D2 ·
¸¸( p h pl ) t 0 ,
¨¨
©1D ¹
i.e., pl Dch is always the highest profit, so it can be concluded that the optimal solution
is given by Wh1
pl .Ŷ
Wl1
From Lemma 9.1 it can be concluded that under Option C, the profits for the Supplier,
Buyer, and the SC can be obtained as:
S1
pl Dc h ; B1
D ( p h pl ) ; and T1 D ( p h ch ) (1 D ) pl .
(9.10)
The options of the Supplier can now be summarized in the following way:
x
Option A : Offer single product at price ph with resulting profit S1
x
Option B : Offer single product at price Wl1
x
Option C: Offer two products at price Wl1
It
can
be
concluded
that
Option
( p l Dp h )
with S1
(1 D )
pl and Wh1
A
is
Dp h ;
( p l Dp h )
;
(1 D )
pl so that: S1
preferred
over
p h Dc h .
Option
C
iff
pl d D ( p h ch ) ; Option A is preferred over Option B iff pl d D (2 D ) p h : and Option B
is preferred over Option C iff pl t ph (1 D )ch . Note that under Assumption (9.1) it
holds that:
D ( p h ch ) d D (2 D ) p h d p h (1 D )ch .
(9.11)
It follows that when pl D ( p h ch ) , the decentralized SC produces a basic product and
sells it to the Highs. Furthermore, if:
D ( p h ch ) d pl d ph (1 D )ch ,
(9.12)
the decentralized SC sells two different products to different consumer segments. Finally,
when pl ! ph (1 D )ch , the decentralized SC stocks only a single product and sells it to
the both the segments. The performance of the decentralized SC is summarized in Figure
9.3.
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CHAPTER
Option A best
Option C best
Option C second best
Option A best
Decentralized channel
Decentralized channel
Option A second best
Option C best
Option C second best
Option B worst
Option A second best
Option B worst
Option B worst
Option B worst
Option C best
Option B best
Option B second best
Option C second best
Option C best
Option B best
PL
Option B second best
Option C second best
Option
A
worst
P
Option A worst
p L
l
Option A worst
Option A worst
Two products
Single product to Highs
Single product to all
Two products
Single product to Highs
D ( PH C H )
Single product to all
PH (1 D )C H
D (2 D ) PH
D ( p h ch )
9
ph (1 D )ch
D ((2 D ) ph
Figure 9.3: Decentralized SC performance
For analysis purposes two situations will be distinguished; in Situation 1 it is assumed
that:
D ( p h ch ) d p h ch ,
(9.13)
and in Situation 2 this does not hold, i.e.,
D ( ph ch ) ! ph ch .
(9.14)
In Figure 9.4 the performance of the centralized and the decentralized SC are compared
under Situation 1.
Single product to Highs
Two products
Single product to all
Two products
Single product to Highs
Single product to all
pl pl
Centralized channel
pl
Decentralized channel
Two products
Two products
Single product
product to
to Highs
Highs
Single
Double
Double
marginalization
marginalization
(understocking)
(understocking)
D
1D
ch
D ( p h ch )
pl
SingleSingle
product
to all to all
product
Double Double
marginalization
marginalization
(overstocking)
(overstocking)
pph hchchph ch
pph h(1(1pD
)c)(hc1h D )ch
hD
Figure 9.4: Centralized versus decentralized SC under Situation 1
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
As can be observed from Figure 9.4, there are two intervals in which the centralized and
the decentralized SC reach different conclusions. If:
D
c h pl D ( p h c h ) ,
1D
(9.15)
the decentralized SC produces a basic product and sells it to the Highs, whereas a
centralized SC produces for both segments (it can be easily verified that the upper bound
of this interval is indeed larger than the lower bound). In other words, this leads to
“under-stocking;” the interval in Equation (9.15) is therefore referred to as the understocking interval. Furthermore, if:
p h ch pl ph (1 D )ch ,
(9.16)
the decentralized SC sells two different products to different consumer segments,
whereas the centralized SC sells one product to both segments. Therefore, the interval in
Equation (9.16) will be referred to as the overstocking interval. Obviously (from the
analysis of the centralized scenario), in both the under-stocking and overstocking interval,
the decentralized SC performs sub-optimally, i.e., leads to a lower profit when compared
to the centralized scenario.
In Figure 9.5, the performance of the centralized and the decentralized SC are compared
under Situation 2.
Two
products
Single product to Highs
Single product to all
Two products
Single product to Highs
Single product to all
pl pl
Centralized channel
pl
Decentralized channel
Single product
Highs to Highs
Singletoproduct
Double
Double
marginalization
marginalization
(understocking)
(understocking)
D
1D
ch
pphh cchh
Wrong
focus
Wrong
focus
pl
Two
Two products
products
SingleSingle
product
to all to all
product
DoubleDouble
marginalization
marginalization
(overstocking)
(overstocking)
pDh))cchh(1 D )ch
DD((pphh ccDhh))( ph ch )pphh ((11D
Figure 9.5: Centralized versus decentralized SC under Situation 2
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9
As can be observed from Figure 9.5, there are three intervals in which the centralized and
the decentralized SC reach different conclusions. If:
D
c h pl p h c h ,
1D
(9.17)
the decentralized SC produces a basic product and sells it to the Highs whereas a
centralized SC produces for both the segments. As before the interval in Equation (9.17)
is referred to as the under-stocking interval. Furthermore, if:
p h c h pl D ( p h c h ) ,
(9.18)
the decentralized SC produces a basic product and sells it to the Highs whereas the
centralized SC sells one product to both segments. Though in both the cases only one
variant is stocked, the centralized SC sells to both segments whereas the decentralized SC
sells only to the Highs. In other words, the decentralized SC is focused on the wrong
segment, which is the reason why the interval in Equation (9.18) is referred to as
unfocused. Finally if:
D ( p h ch ) pl ph (1 D )ch ,
(9.19)
the decentralized SC sells two different products to different consumer segments whereas
the centralized SC sells one product to both the segments. As earlier, the interval in
Equation (9.19) will be referred to as the overstocking interval. Again, it follows directly
from the analysis of the centralized scenario that in all the three cases the decentralized
SC performs sub-optimally, i.e., leads to a lower profit when compared to the centralized
scenario.
To provide clarity on the insights from the analysis in different scenarios we consider the
following 10 numerical examples throughout this chapter.
Example
For Examples [1]-[5] we consider ph = €10, Į = 0.6 and ch = €1. The pl values for
Examples [1] to [5] are considered to be €1, €5, €7, €9.5 and €9.8 respectively. Note that
Examples [1]-[5] satisfy the condition for Situation 1.
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For Examples [6]-[10] it is assumed that ph = €10, Į = 0.6 and ch = €3. The pl values for
Examples [6] to [10] are considered to be €4, €6, €7.5, €8, and €9 respectively. Clearly,
Examples [6]-[10] satisfy the condition for Situation 2. The performances of the
centralized and the solitaire scenarios are summarized in Table 9.1.
Centralized SC
Decentralized SC
Exam
Product variants
SC
Product variants
Buyer’s
Supplier’s
SC
ple #
decision
profit
decision
profit
profit
profit
€0.0
€6.0
€6.0
€0
€6.0
€6.0
€1.8
€6.4
€8.2
€1.8
€6.4
€8.2
€0.3
€9.5
€9.8
€0.0
€6.0
€6.0
€0.0
€6.0
€6.0
€0.0
€6.0
€6.0
€1.2
€6.2
€7.4
€1.5
€7.5
€9.0
1
pl =€1.0
2
pl =€5.0
Sell single product to
highs
€6.0
Sell two different
products to different
ch =€1
products to different
€8.2
segments
pl =€9.5
4
pl =€9.8
5
6
pl =€4.0
7
pl =€6.0
Sell a single product
to both the segments
Sell a single product
to both the segments
Sell single product to
highs
ch =€3
pl =€7.5
pl =€8.0
9
10
pl =€9.0
Sell a single product
to both the segments
Sell a single product
to both the segments
Sell a single product
to both the segments
products (Coordinated)
products
(over stocking)
Sell a single product to
€9.8
both the segments
(Coordinated)
€6.0
Sell single product to
highs (Coordinated)
Sell a single product to
€6.6
segments
8
Sell two different
Sell two different
€9.5
Sell two different
products to different
highs
(under-stocking)
Sell two different
pl =€7.0
highs (Coordinated)
Sell single product to
€7.4
segments
3
Sell single product to
the Highs
(under-stocking)
Sell a single product to
€7.5
the High’s
(unfocussed)
Sell two different
€8.0
products
(overstocking)
Sell a single product to
€9.0
both the segments
(Coordinated)
Table 9.1: Centralized vs. decentralized results (Numerical example)
It is clear from the above table in Examples [2] and [7], the decentralized scenario leads
to an under-stocking situation. In, Example [8], the decentralized SC has an unfocused
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9
strategy and in Examples [4] and [9], the decentralized scenario leads to a overstocking
situation.Ŷ
The above observations are summarized in the following theorem.
Theorem 9.2
If D ( p h ch ) d p h ch then
(i) if
D
ch pl D ( p h c h ) , then in a decentralized SC the Buyer stocks a basic
1D
product and sells it to the Highs segment, whereas the centralized SC sells two
different variants to different segments. As a result, this leads to a lower profit
for the entire SC.
(ii) if p h ch pl ph (1 D )ch , then in a decentralized SC the Buyer stocks two
different products and sells them to different segments whereas the centralized
SC stocks the basic product and sells it to both segments. As a result, this
leads to a lower profit for the entire SC.
If D ( p h ch ) ! p h ch , then:
(iii) if
D
ch pl ph ch then in the decentralized SC the Buyer stocks a basic
1D
product and sells it to the Highs segment, whereas the centralized SC sells two
different variants to different segments. As a result, this leads to a lower profit
for the entire SC.
(iv) if p h ch pl D ( p h C h ) then in a decentralized SC the Buyer stocks a basic
product and sells it to the Highs segment, whereas the centralized SC sells the
basic product to different segments. As a result, this leads to a lower profit for
the entire SC.
(v) if D ( p h ch ) pl p h (1 D )ch then in a decentralized SC the Buyer stocks two
different products and sells them to different segments, whereas the
centralized SC stocks the basic product and sells it to both segments. As a
result, this leads to a lower profit for the entire SC.
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
235
From the detailed analysis performed on the decentralized scenario it is clear that the
under-stocking interval for Situation 1 is
is
D
1D
D
1D
ch pl D ( p h c h ) and for Situation 2
c h pl p h ch . Though the parameter values for which the decentralized SC
under-stocks are different for the two situations, the players’ decisions and their profit
functions are the same under both situations. Therefore, in the remainder of this chapter
when referring to the under-stocking interval, it refers to both situations. In other words,
the solutions obtained and insights derived for under-stocking in fact are applicable for
both Situation 1 and Situation 2. Similarly, the overstocking interval for Situation 1 is
p h ch pl p h (1 D )ch and for Situation 2 it is D ( p h ch ) pl ph (1 D )ch .
However, when referring to the overstocking interval, it refers to both situations.
In the next section we design different contract mechanisms to test their abilities to
coordinate the product variant decisions in all regions mentioned and provide win-win
opportunities.
We design three different contracts, namely the slotting allowance, revenue sharing and
profit sharing mechanisms to achieve coordination and win-win opportunities. In the next
section we design the slotting mechanism.
9.5
Slotting allowance mechanism
Slotting allowances (which will be denoted by subscript 2) are lump-sum payments made
by the Supplier to the Buyer for stocking additional variants. Let ș2 be the slotting
allowance paid by the Supplier to the Buyer if and only if the Buyer stocks both variants.
As before, the Supplier sets the wholesale price for the two different variants at Wl 2 and
Wh2 . As such, the slotting allowance contract consists of three parameters and is denoted
by [Wl 2 ;Wh2 ;T 2 ] . The key idea of the slotting allowance contract is that if the Supplier
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9
offers a slotting allowance to the Buyer, the Buyer might be willing to stock both items,
which, as witnessed by Theorem 9.2, in some cases can lead to a higher profit for the SC.
By carefully choosing the value of ș2, it might be ensured that both the Buyer and
Supplier benefit from such a contract.
The following theorem shows the ability of the slotting allowance contract in providing
coordination and win-win. Theorem 9.3 summarizes the performance of the slotting
allowance mechanism.
Theorem 9.3
For all values of pl in the under-stocking interval, there is a slotting allowance contract
[Wl2* ,Wh*2 T 2 ] such that:
(i) the SC is coordinated;
(ii) win-win opportunities are achieved.
Proof
(i) As before, the Buyer has the following three options:
Option 1:
Sell the basic product to the Highs at price ph. In this case his profit is equal
to B2
Option 2:
D ( p h Wl ) .
2
Sell the basic product to both segments at price pl. In this case the profit is
given by B2
Option 3:
pl Wl2 .
Sell two different products to different segments. Under this option the
profit of the Buyer is given by B 2 D ( p h Wh2 ) (1 D )( pl Wl2 ) T 2 .
The Supplier also has 3 options:
Option A:
Offer a single product targeted at the Highs at the optimal wholesale price
Wl2
Option B:
p h . In this case the Supplier’s profit is given by S 2
Dp h .
Offer a single product targeted to both the segments. Now the Supplier
wants to set a price Wl2 such that his own profit is maximized. From the
Inside_proefschrift_Vijayender_06.indd 236
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237
USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
analysis of the solitaire scenario we know that when Wl2
( p l Dp h )
, the
(1 D )
Buyer sells the single product to both the segments. The resulting Supplier
profit can be obtained as: S 2
Option C:
( p l Dp h )
.
(1 D )
Offer two products at prices Wl2*
p h and Wh*2
p h , and reward the Buyer
with a slotting allowance ș2. Note that in fact a specific slotting allowance
contract is selected here, namely [Wl2*
p h ;Wh*2
p h ;T 2 ] . Under this option,
the Buyer makes the following profits with his different options: Option 1:
B2 = 0; Option 2: B2
pl p h 0 ; Option 3: B2
(1 D )( pl ph ) T 2 .
Clearly, to ensure that the Buyer will sell two different products to different
segments, ș2 must be set such that:
T 2 ! (1 D )( ph pl ) : T 2 .
(9.20)
Under this condition the profit for the Supplier with Option C is given as:
S2
p h Dc h T 2 .
As shown under the solitaire scenario, since pl D ( p h ch ) d D (2 D ) p h , the Supplier
prefers Option A over Option B. To ensure that Option C is preferred over option A, the
following condition must be fulfilled:
T 2 (1 D ) ph Dch : T 2 .
It is easy to see that T 2 ! T 2 if and only if pl !
(9.21)
D
1D
c h . This condition is always true
since, from Equations (9.15) and (9.17), the under-stocking is encountered in both
Situations 1 and 2 only when pl !
D
c h . It can be concluded that under the condition
1D
T 2 T 2 T 2 , the Supplier will offer two products at wholesale prices Wl *
2
Wh*2
p h , and will have profit S 2
p h and
p h Dc h T 2 . Furthermore, in this situation the
Buyer will stock both products and have profit B2
(1 D )( pl p h ) T 2 . It follows that
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CHAPTER
the SC profit is given by T2
9
D ( p h ch ) (1 D ) pl , which is equal to the
S 2 B2
profit in the centralized SC in the under-stocking interval, i.e., the SC is coordinated.
(ii) Under the slotting allowance contract [Wl2*
p h ;Wh*2
p h ;T 2 ] with T 2 T 2 T 2 , the
Buyer reaches a higher profit when compared to the solitaire scenario iff
(1 D )( pl ph ) T 2 ! 0, i.e., iff T 2 ! (1 D )( ph pl )
T 2 .
Furthermore, the Supplier reaches a higher profit when compared to the solitaire scenario
iff ph Dch T 2 ! Dph , i.e., iff T 2 (1 D ) ph Dch
T 2 .Ŷ
The performance of the centralized and the decentralized SC with the slotting allowance
mechanism for Situation 1 is summarized in Figure 9.6.
Single product to Highs
Two products
Two products
Single product to Highs
Single product to all
Single product to all
plpl
Centralized channel
T
T T DD( p( hp
chc)h ) (1(
1 DD) p) lpl
h Dp h
T
plT
pl
pl
Slotting allowance
pl
BB (1(1DD)()(ppl lpph )h )TT
BB 0 0
S S DD
phph
SS pph hDDchchTT
Two
TT SSBB DD( (pph hchc)h )(1(1DD) )ppl l products
Two productsSingle
product
to allto all
Single
product
T T DD
phph
Twoproducts
products
Two
Singleproduct
producttotoHighs
Highs
Single
D
1D
ch
Double
Double
marginalization
marginalization
(overstocking)
(overstocking)
p h ch p h ch
DD( (pph hchc)h )
ph (1 phD)c(1h D )ch
Figure 9.6: Centralized versus slotting allowance mechanism (Situation 1)
As can be observed from Figure 9.6 that the centralized SC and the decentralized SC with
the slotting allowance mechanism sell two different products to different segments
if
D
ch pl D ( p h c h ) . However, if p h ch pl ph (1 D )ch , the Buyer with
1D
the slotting allowance mechanism sells two different products to different consumer
segments whereas the centralized SC sells one product to both segments. To summarize:
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
239
for Situation 1, the slotting allowance mechanism can eliminate the double
marginalization in the under-stocking region but does not eliminate the double
marginalization in the overstocking region. It is easy to see that the same holds for
Situation 2. More precisely, in Situation 2 the slotting allowance mechanism can
eliminate the double marginalization in the under-stocking region but cannot eliminate
the double marginalization in the unfocused and overstocking regions.
Example (continued)
The results of the slotting allowance for the numerical examples are summarized in Table
9.2.
Note that in Examples [2] and [7], the slotting allowance mechanism provides
coordination and win-win and eliminates the under-stocking situation. However, in
Example [8], the slotting allowance cannot eliminate the double marginalization due to a
unfocused condition. Moreover, in Examples [4] and [9], the slotting allowance cannot
eliminate the overstocking situation.Ŷ
In the next section we design the revenue sharing mechanism.
9.6
Revenue sharing mechanism
In the revenue sharing mechanism (which will be denoted by subscript 3), the
transactions between the Supplier and the Buyer are governed by the Supplier receiving a
share of the Buyer’s revenues. The revenue sharing mechanism consists of three
parameters and is denoted by [Wl3 ;Wh3 ; J 3 ] . Wl3 and Wh3 are the wholesale prices set by
the Supplier for two different variants, and J3 (0 < J3 < 1) is the percentage of the Buyer’s
revenue that goes to the Supplier.
The following theorem summarizes the performance of the revenue sharing mechanism.
239
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Inside_proefschrift_Vijayender_06.indd 240
ch =€3
ch =€1
#
pl =€9.0
10
pl =€6.0
7
pl =€8.0
pl =€4.0
6
9
pl =€9.8
5
pl =€7.5
pl =€9.5
4
8
pl =€7.0
pl =€5.0
2
3
pl =€1.0
1
Example
€9.0
€8.0
€7.5
€6.6
€6.0
€9.8
€9.5
€8.2
€7.4
€1.5
€1.2
€0.0
€0.0
€0.0
€0.3
€1.8
€1.8
€0.0
€0.0
profit
Buyer’s
€7.5
€6.2
€6.0
€6.0
€6.0
€9.5
€6.4
€6.4
€6.0
€6.0
profit
Supplier’s
€9.0
€7.4
€6.0
€6.0
€6.0
€9.8
€8.2
€8.2
€6.0
€6.0
SC profit
Decentralized SC
Coordinated
Overstocking
Unfocussed
Assume ș =1.9 (mid-interval)
win-win range is 1.6 < ș < 2.2
Coordinated
Coordinated
Coordinated
Overstocking
Coordinated
Assume ș =2.7 (mid-interval)
win-win range is 2 < ș < 3.4
Coordinated
Coordinated
parameter values for win-win.
to centralized SC and the
€1.5
€1.2
€0.0
€ 0.3
€0.0
€0.3
€1.8
€1.8
€0.7
€7.5
€6.2
€6.0
€ 6.3
€6.0
€9.5
€6.4
€6.4
€6.7
€6.0
profit
profit
€0.0
Supplier’s
Buyer’s
Slotting allowance mechanism [Wl= €10; Wh = €10; ș]
Product variant decisions relative
Table 9.2: Results for the slotting allowance (Numerical example)
both the segments
Sell a single product to
both the segments
Sell a single product to
both the segments
Sell a single product to
segments
products to different
Sell two different
highs
Sell single product to
both the segments
Sell a single product to
both the segments
Sell a single product to
segments
products to different
Sell two different
segments
products to different
Sell two different
highs
€6.0
profit
decision
Sell single product to
SC
Product variants
Centralized SC
€9.0
€7.4
€6.0
€6.6
€6.0
€9.8
€8.2
€8.2
€7.4
€6.0
profit
SC
240
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
Theorem 9.4
(i) The revenue sharing contract with [Wl3*
0;Wh*3
(1 J 3 )c h ; J 3 ] will lead to a
coordinated SC for all J 3 .
(ii) For all pl in the under-stocking interval, win-win is achieved with the revenue
sharing contract [Wl3*
Dp h
D ( ph ch ) (1 D ) pl
0;Wh*3
(1 J 3 )c h ; J 3 ] iff:
d J 3 d 1.
(iii)For all pl in the unfocused interval, win-win is achieved with the revenue sharing
contract [Wl3*
0;Wh*3
(1 J 3 )ch ; J 3 ] iff
Dp h
pl
d J3 d1
(iv) For all pl in the overstocking interval, win-win is achieved with the revenue
sharing contract [Wl3*
0;Wh*3
(1 J 3 )c h ; J 3 ] iff:
p l Dc h
p D ( p h pl )
d J3 d l
.
pl
pl
Proof
Assume that the Supplier offers a revenue sharing contract [Wl3*
0;Wh*3
(1 J 3 )ch ; J 3 ]
to the Buyer.
(i) As before, the Buyer has the following three options:
(1 J 3 )Dph .
Option 1:
Sell the basic product to the Highs at price ph for a profit of B3
Option 2:
Sell the single product to both the segments at price pl for a profit of
B3
Option 3:
(1 J 3 ) pl .
Sell two different products to different segments at prices ph and pl. Under
this option the profit for the Buyer is B 3 (1 J 3 )[D ( p h ch ) (1 D ) pl ] .
It follows that the Buyer chooses Option 1 if pl and Option 3 if
D
1D
D
ch , Option 2 if pl ! ( ph ch ) ,
1D
ch d pl d ph c h . Note that the Buyer’s preferred options for
241
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CHAPTER
9
different parameter values are the same as that of the centralized SC. The Supplier’s
profits
[Wl3*
with
0;Wh*3
Option A:
the
options
with
the
revenue
sharing
contract
If the Buyer sells the single product to the Highs the profit for the Supplier
J 3Dp h .
When the Buyer targets a single product to both the segments the Supplier’s
J 3 pl .
profit is S 3
Option C:
different
(1 J 3 )ch ; J 3 ] can be obtained as follows:
is S 3
Option B:
3
If the Buyer offers two different products to different segments, the
Supplier’s profit can be obtained as S 3 J 3 [D ( p h c h ) (1 D ) pl ] .
The SC profit with Option A is B3 S 3
Option C: B3 S 3
Dp h , with Option B: B3 S 3
pl , and with
D ( p h ch ) (1 D ) pl . Since the SC profit with each of the options
is same as that of the centralized scenario, it follows immediately that the revenue sharing
contract [Wl3*
0;Wh*3
(1 J 3 )c h ; J 3 ] coordinates the SC for all J 3 .
(ii) In the under-stocking region, the profits for the Supplier, Buyer, and SC in the
decentralized SC are: S1
Dp h ; B1
Dph , see Equation (9.4). The profit for
0 ; and T1
the Supplier with the revenue sharing will be greater than the profit in the decentralized
SC if J 3[D ( ph ch ) (1 D ) pl ] ! Dph , i.e., when:
J3 !
Dph
[D ( ph ch ) (1 D ) pl ]
(9.22)
: J 3 .
The profit for the Buyer under the revenue sharing contract will be greater than the profit
in the decentralized SC if (1 J 3 )[D ( ph ch ) (1 D ) pl ] ! 0 , i.e., when:
(9.23)
J 3 1 : J 3 .
It is easy to see that J 3 J 3 t 0 if and only if pl !
D
1D
c h . From Equations (9.15) and
(9.17) it follows that this condition is always true since under-stocking is encountered in
both Situation 1 and Situation 2 only when pl !
D
ch .
1D
242
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
243
(iii) In the unfocused region, the profits for the Supplier, Buyer and the SC in the
decentralized SC are: S1
Dp h ; B1
0 ;and T1
Dp h , see Equation (9.15). The profit for
the Supplier with the revenue sharing will be greater than the profit in the decentralized
SC if J 3 pl ! Dph , i.e., when:
J3 !
D ph
Pl
: J 3 .
(9.24)
The profit for the Buyer under the revenue sharing contract will be greater than the profit
in the decentralized SC if (1 J 3 ) pl ! 0 . i.e., when:
J 3 1 : J 3
(9.25)
The condition J 3 J 3 ! 0 is true if pl ! Dph . If this condition is not true, then the
centralized SC also prefers to sell a single product to Highs and the possibility of an
unfocused interval does not arise, see Equation (9.2).
(iv) In the overstocking region, the profits for the Supplier, Buyer, and the SC in the
decentralized SC are S1
pl Dc h ; B1
D ( p h pl ) and T1 D ( p h ch ) (1 D ) pl , see
Equation (9.10). The profit for the Supplier with revenue sharing will be greater than the
profit in the decentralized SC if J 3 pl ! pl Dch , i.e., when:
J3 !
pl Dch
: J 3 .
pl
(9.26)
The profit for the Buyer with the revenue sharing will be greater than the profit in the
decentralized SC (1 J 3 ) pl ! D ( ph pl ) , i.e., when:
J3 pl D ( ph pl )
: J 3 .
pl
(9.27)
The condition J 3 J 3 ! 0 is true if and only iff: pl ! ph ch . This condition is always
true since, by Equations (9.16) and (9.17), overstocking is encountered in both Situations
1 and 2 only when pl ! ph ch .Ŷ
The performance of the centralized and the decentralized SC under the revenue sharing
mechanism is summarized in Figure 9.7. As can be observed, the decentralized SC under
243
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CHAPTER
9
the revenue sharing mechanism performs the same as the centralized SC in all regions
and for all parameter values.
Single product to Highs
Single product to Highs
Two products
Two products
Single product to all
Single product to all
pl pl
Centralized channel
T
T
Dp h
D ( ph ch ) (1 D ) pl
T
pl
pl
Revenue sharing
Two products
Single product to Highs
Single product to Highs
B (1 J )Dph
B
Single product to all
Single product to all
B (1 J ) pl
B S(1 JJ[D)[(Dp(hph ch c) h) (1 (1D)Dp)l p] l ]
B S (1 JDJp)D
p
h h
Dpphh
ST JD
T
Two products
(1 J )[D ( ph ch ) (1 D ) pl ]
B S (1 JpJl ) pl
ST Jppll
ST J[[DD((pphh cchh))((11DD))ppl l ]]
Dph
T
D
ch
1
DD
1D
ch
pl
T
[D ( ph ch ) (1 D ) pl ]
pl
p h ch
p h ch
Figure 9.7: Centralized versus revenue sharing mechanism
Example (continued)
The results of the revenue sharing mechanism for the numerical examples are
summarized in the Table 9.3.
It is clear from the above results that the suggested revenue sharing contract provides
coordination for all the numerical examples for which the decentralized SC does not. The
range of J for which win-win can be achieved is obtained for each example. In all
relevant cases, the mid-interval J value (of the win-win range) is chosen to calculate the
profits for the Buyer and the Supplier.Ŷ
Inside_proefschrift_Vijayender_06.indd 244
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Inside_proefschrift_Vijayender_06.indd 245
ch =€3
ch=€1
#
pl =€9.0
10
pl =€6.0
7
pl =€8.0
pl =€4.0
6
9
pl =€9.8
5
pl =€7.5
pl =€9.5
4
8
pl =€7.0
pl =€5.0
2
3
pl =€1.0
1
Example
€9.0
€8.0
€7.5
€6.6
€6.0
€9.8
€9.5
€8.2
€7.4
€1.5
€1.2
€0.0
€0.0
€0.0
€0.3
€1.8
€1.8
€0.0
€0.0
profit
Buyer’s
€7.5
€6.2
€6.0
€6.0
€6.0
€9.5
€6.4
€6.4
€6.0
€6.0
profit
Supplier’s
Decentralized SC
€9.0
€7.4
€6.0
€6.0
€6.0
€9.8
€8.2
€8.2
€6.0
€6.0
profit
SC
Revenue sharing mechanism
Coordinated
0.78 < J < 0.85. Assume J = 0.82
Coordinated and win-win is achieved for
0.8< J < 1. Assume J = 0.9
Coordinated and win-win is achieved for
0.91< J < 1. Assume J = 0.95
Coordinated and win-win is achieved for
Coordinated
Coordinated
0.94< J < 0.97. Assume J = 0.95
Coordinated and win-win is achieved for
Coordinated
0.81< J < 1. Assume J = 0.90
Coordinated and win-win is achieved for
Coordinated
values for win-win
centralized SC and the parameter
Product variant decisions relative to
€1.5
€1.4
€0.8
€0.3
€0
€0.3
€ 0.5
€1.8
€0.7
€7.5
€ 6.6
€6.7
€ 6.3
€6
€9.5
€ 9.0
€6.4
€ 6.7
€6
profit
profit
€0
Supplier
Buyer
J J
and [Wl= 0; Wh = 3(1-J); J] when ch =€3)
€9
€8
€7.5
€6.6
€6
€9.8
€9.5
€8.2
€7.4
€6
profit
SC
J J
(Coordinating contract is [Wl= 0; Wh = (1-J); J] when ch =€1
Table 9.3: Results for the Revenue sharing (Numerical example)
both the segments
Sell a single product to
both the segments
Sell a single product to
both the segments
Sell a single product to
segments
products to different
Sell two different
highs
Sell single product to
both the segments
Sell a single product to
both the segments
Sell a single product to
segments
products to different
Sell two different
segments
products to different
Sell two different
highs
€6.0
profit
decision
Sell single product to
SC
Product variants
Centralized SC
USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
245
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246
9.7
CHAPTER
9
Profit sharing mechanism
In the profit sharing mechanism (which will be denoted by subscript 4), the transactions
between the Supplier and the Buyer are governed by the Supplier receiving a share of the
Buyer’s profits. The profit sharing mechanism consists of three parameters and is denoted
by [Wl4 ;Wh4 ; G 4 ] , where Wl4 and Wh4 are the wholesale prices set by the Supplier for two
different variants, and G4 (0 < G4 < 1) is the percentage of the Buyer’s profit that goes to
the Supplier.
The following theorem establishes an equivalence relationship between the revenue and
profit sharing mechanisms.
Theorem 9.5
If J 3
G 4 , then the revenue sharing contract [Wl*
3
sharing contract [Wl4*
0;Wh*4
0;Wh*3
(1 J 3 )ch ; J 3 ] and the profit
ch ; G 4 ] result in the same profits for the Buyer, Supplier
and SC.
Proof
Assume the Supplier offers a profit sharing contract [Wl4*
0;Wh*4
ch ; G 4 ] to the Buyer.
As before, the Buyer has the following three options:
Option 1:
Sell the basic product to the Highs at price ph. In this case his profit is equal
to B4
Option 2:
(1 G 4 )Dph .
Sell the single product to both segments at price pl. In this case the profit is
given by B4
Option 3:
(1 G 4 ) pl .
Sell two different products to different segments. Under this option the
profit of the Buyer is given by B 4 (1 G 4 )[D ( p h ch ) (1 D ) pl ] .
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
As the Buyer’s preferred option for different parameter values is same as that in the
centralized SC, he chooses Option 1 if pl Option 3 if
D
1D
D
1D
ch , Option 2 if pl ! ( ph ch ) , and
ch d pl d ph ch .
When the Supplier offers a profit sharing contract [Wl4*
0;Wh*4
ch ; G 4 ] to the Buyer, the
Supplier’s profits with the 3 different options can be obtained as follows:
Option A:
If the Buyer sells the single product to the Highs, the profit for the Supplier
is given by S 4
Option B:
G 4Dph .
When the Buyer targets a single product to both segments, the Supplier’s
profit is given by S 4
Option C:
G 4 pl .
If the Buyer offers two different products to different segments, the
Supplier’s profit is given by S 4 G 4 [D ( p h ch ) (1 D ) pl ] .
It follows that the SC profit with Option A is B4 S 4
B4 S 4
pl , and with Option C is B4 S 4
immediately that if J 3
Dp h , with Option B is
[D ( p h ch ) (1 D ) pl ] . It follows
G 4 , the profits for the Buyer, Supplier, and the SC with the
revenue and profit sharing mechanisms are the same. Ŷ
The following corollary summarizes the performance of the profit sharing mechanism.
Corollary 9.6
(i) A profit sharing contract with [Wl4*
0;Wh*4
ch ; G 4 ] will lead to a coordinated SC
for all G 4 .
(ii) For all pl in the under-stocking interval, win-win is achieved with the profit
sharing contract [Wl4*
0;Wh*4
ch ; G 4 ] iff
Dp h
D ( ph ch ) (1 D ) pl
d G4 d1.
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(iii) For all pl in the unfocused interval, win-win is achieved with the profit sharing
contract [Wl4*
0;Wh*4
ch ; G 4 ] iff
Dp h
pl
d G4 d1
(iv) For all pl in the overstocking interval, win-win is achieved with the profit sharing
contract [Wl4*
0;Wh*4
ch ; G 4 ] iff
p l Dc h
p D ( p h pl )
.
d G4 d l
pl
pl
Proof
Follows directly from Theorem 9.4 and 9.5.Ŷ
The next section concludes this study and provides direction for future research.
9.8
Conclusions
In this chapter a detailed analysis of the double marginalization of product line decisions
is provided. When the end-consumers are comprised of two segments with a different
willingness-to-pay, it is shown that a decentralized SC can either stock the same, a lower,
or higher number of product variants when compared to a centralized SC. Under certain
conditions the decentralized SC can also have a wrong focus, whereby it sells a single
product to the Highs when a centralized SC would sell a single product to both segments.
The decision of the decentralized SC to stock less, more, or to have a wrong focus (when
compared to the centralized SC) depends on the parameter settings like willingness-topay of different segments, segment size and the costs associated with producing different
variants. It is shown that the slotting allowance mechanism can coordinate and provide
win-win opportunities in a region where the decentralized SC stocks a less than optimal
number of product variants. However, it is also demonstrated that the slotting allowance
mechanism fails to coordinate the SC in a situation where the decentralized SC stocks a
higher than optimal number of product variants or when the decentralized SC has a
wrong focus. To overcome such difficulty, we design the revenue and profit sharing
mechanisms and show that coordination and win-win opportunities are achieved for all
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USING CONTRACT MECHANISMS TO COORDINATE PRODUCT LINE DECISIONS
249
parameter values. Moreover, an equivalence relationship is established between the
revenue and profit sharing mechanisms.
This study offers ample scope for further research. One possible extension is to add a
dimension of uncertainty to the willingness-to-pay of different consumer segments. The
introduction of information asymmetry (for example only the Buyer knows the
willingness-to-pay with certainty, whereas the Supplier knows the probability distribution
of the willingness-to-pay of the end-consumers) is also of interest and practical relevance.
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CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
Chapter 10
Conclusions and Directions for Future Research
In this dissertation, we have made contributions through design and analysis of contract
mechanisms to coordinate a variety of operational and marketing decisions such as
pricing and replenishment, promotions, service-level and assortment decisions. This is
one of the first studies, in which the issue of win-win opportunity in the process of
aligning SC decisions has been addressed explicitly. Furthermore, the relationship
between different contract mechanisms is brought out wherever possible.
This chapter presents the conclusions on the different research questions posed in Chapter
1, using the framework as given in Figure 10.1.
SC structure
Product characteristics
Demand characteristics
Supply characteristics
Operational decisions
Contracts
Mechanisms
Replenishment decision
Product line decisions
Marketing decisions
Coordination
&
Win-win
Pricing decisions
Promotional decisions
Service level decisions
Product line decisions
Figure 10.1: Research framework with different decisions discussed in this thesis
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This chapter is organized as follows. In the next section, we draw general conclusions for
each decision and discuss the performance of different contract mechanisms under
different SC settings. Later, we provide an overall conclusion based on the central
problem statement of this dissertation. Subsequently, we briefly touch upon the
implementation issues. Finally, we provide directions for further research.
10.1 Research findings and conclusions
Detailed conclusions on each study are presented in the respective chapters and the
overview of the key results is given in Table 10.1.
Below we highlight some key results for each decision and discuss the performance of
different contract mechanisms under different SC scenarios.
10.1.1 Coordinating pricing and replenishment decisions in a SC (Part I)
For the pricing and replenishment decisions, we have considered four different SC
settings each with different demand and cost conditions. In each of the four settings, we
have considered a single period short life cycle product. A brief explanation of each
setting is given below.
[1]
In Chapter 3, we consider a two-echelon SC in which the end-consumer demand is
price sensitive and deterministic. The Supplier incurs a fixed marginal cost for
producing and distributing each unit demanded by the Buyer.
[2]
In Chapter 4, both the Buyer and the Supplier incur increasing marginal costs,
which are represented by quadratic functions of the ordered/produced quantities.
The final selling price of the product is fixed.
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Part 4
Part 3
Part 2
Part 1
Chapter 3
Coordination
Win-win
Chapter 4
Coordination
Win-win
Chapter 5
Coordination
Win-win
Chapter 6
Coordination
Win-win
Chapter 7
Coordination
Win-win
Chapter 8
Coordination
Win-win
Chapter 9
Coordination
Win-win
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
-
Yes
Yes
-
-
-
Yes
Yes
Yes
Yes
Quantity
discount
-
Yes
Yes
-
Yes
Yes
-
Yes
Yes
Yes
Yes
License
Fee
No
No
-
-
-
-
-
-
Slotting
-
-
-
Yes
Yes
-
-
-
Buyback
-
-
Yes
No
-
-
-
-
Mail-inrebate
Table 10.1: Summary of the performance of contract mechanisms
Yes
Yes
No
Yes
-
Yes
Yes
Yes
No
-
Yes
Yes
Profit sharing
Yes
Yes
Revenue
sharing
-
-
No
No
-
-
-
-
Wholesale
price
discount
-
-
Yes
Yes
-
-
-
-
Combined rebate
mechanism
CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
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[3]
CHAPTER
10
In Chapter 5, a SC model with two consumer segments, each with their own
willingness-to-pay is considered.
[4]
In Chapter 6, the end-consumer demand is uncertain. As in Setting [1], the Supplier
incurs a fixed marginal cost.
In each of the four settings, we have analyzed both the revenue and profit sharing
mechanisms. Our main findings are:
1. The profit sharing mechanism is robust, in the sense that the performance of the profit
sharing mechanism is not affected by the demand and cost conditions considered in
the four settings. The profit sharing mechanism coordinates and leads to win-win
opportunities simultaneously in all the four settings considered above.
2. The performance of the revenue sharing mechanism is sensitive to the demand and
cost conditions considered. The revenue sharing mechanism coordinates and leads to
win-win opportunities simultaneously in all the settings except for a setting in which
the costs were marginally increasing and the final selling price was fixed (i.e., for
Setting [2]).
From a robustness point of view, the profit sharing mechanism appears to be superior to
the revenue sharing mechanism. However, from an implementation point of view, the
revenue sharing mechanism will be simpler compared to the profit sharing since the
profit figures of different companies are not often shared unambiguously. This motivates
us to analyze the equivalence relationship between these two contract mechanisms. Our
main findings are:
1. In all the three settings (Settings [1], [3] & [4]), where the revenue sharing
mechanism provides both coordination and win-win opportunities, we could establish
an equivalence relationship between the revenue and profit sharing mechanisms. This
equivalence relationship enables the players to choose one mechanism over the other
without losing its effectiveness. For instance, in a situation where the Buyer does not
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CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
share his profit information unambiguously, the Supplier can opt for the revenue
sharing mechanism without compromising either on coordination or win-win
opportunities. And also from an implementation perspective, the revenue sharing
mechanism is an easier metric to evaluate, and the profit figures of different
organizations are often disputed. However, while making a choice of one mechanism
over the other, the Supplier has to be careful in fixing the wholesale price parameter
appropriately.
In addition to the profit sharing and revenue sharing mechanisms, we have analyzed the
quantity discount mechanism and the license fee mechanism specifically in the first two
settings. Unlike the revenue sharing mechanism, the latter two contract mechanisms are
not sensitive to the marginally increasing cost factor.
In the next subsection, we make an effort to bring out the general conclusions for
coordinating promotional decisions.
10.1.2 Coordinating promotional decisions in a SC (Part 2)
We considered a SC setting in which the end-consumer demand is price sensitive and
deterministic. The wholesale price rebate and the mail-in-rebate which are commonly
used in practice do not provide coordination and win-win at the same time. In this study,
we designed the so-called combined rebate mechanism and demonstrated its ability to
provide both coordination and win-win opportunities. The combined rebate mechanism
has two parameters, one is the discount provided by the Buyer to the end-consumer and
the other a wholesale price discount provided by the Supplier to the Buyer. This is the
only contract in our study for which the contract parameters are agreed upon after the
wholesale and the final selling price are fixed. The reason is that in practice rebates given
during the promotion are decided based on the current wholesale price. This study helps
us to conclude that in the considered setting, coordination and win-win opportunities can
be achieved only with the two parameters as designed in this study.
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10.1.3 Coordinating price and service-level decisions in a SC (Part 3)
We have considered a two stage SC in which the end-consumer demand is influenced by
the price of the product and by the service-level provided at the Buyer’s outlet. We have
designed and analyzed the revenue sharing, profit sharing, quantity discount and the
license fee mechanism. The profit sharing, quantity discount and license fee mechanisms
do coordinate and provide win-win opportunities simultaneously. The revenue sharing
mechanism does not coordinate the service-level decision, but provides win-win
opportunities for all parameters values. The existence of win-win opportunities is because
of the fact that the revenue sharing coordinates the pricing decision for all parameter
values. However, the revenue sharing mechanism does not coordinate the service-level
decisions because the Buyer incurs all the costs for service provision, while the Supplier
shares a part of the Buyer’s revenues without sharing any of his costs. Clearly, the Buyer
does not have enough motivation/incentive for providing full service when the cost of
service provision is high. On the contrary, with the profit sharing mechanism since the
Buyer shares his profits, his costs for service provision are compensated well enough and
hence the favorable result of both coordination and win-win opportunities.
10.1.4 Coordinating product line decisions in a SC (Part 4)
This study addressed the product line decisions in a SC with a Buyer and a Supplier. The
end-consumers are comprised of two segments with a different willingness-to-pay. The
final demand and the each segment’s willingness-to-pay are assumed to be deterministic.
This study analyzed the slotting allowance mechanism in addition to the revenue and
profit sharing mechanisms.
Though the slotting allowance is very commonly used in practice, our study showed that
it does not coordinate the product line decisions and win-win opportunities for all
parameter values in a two-echelon SC. However, the revenue and profit sharing
mechanisms provide both coordination and win-win opportunities. An equivalence
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257
relationship is established between the parameters of revenue and the profit sharing
mechanisms. However, from an implementation point of view, the revenue sharing
mechanism will be simpler compared to profit sharing since the profit figures of different
companies are not often shared truthfully.
10.2 Overall conclusions
The central problem statement (as given in Section 1.6) of this dissertation is: Can we use
contracts to coordinate operational and marketing decisions across organizations under
different demand and supply conditions and achieve a win-win situation?
As mentioned, in this dissertation we have studied a range of operational and marketing
decisions such as the pricing and replenishment, promotions, service-level and
assortments. Furthermore, we have analyzed the above decisions in a wide variety of
demand and supply conditions, i.e., in a variety of SC settings. For each decision
problem, we have designed and analyzed a variety of contract mechanisms to address the
issue of coordination and win-win. It can be concluded that in all the cases considered, it
is possible to design at least one contract mechanism which can coordinate and provide
win-win opportunities. In this sense the problem statement can be answered by “yes”.
Table 10.1 helps us to provide an overall conclusion on the performance of different
contract mechanism as follows:
1. Profit sharing mechanism coordinates and provides win-win opportunities for all
the settings and decisions, other than the promotional decisions for which it has
not been analyzed.
2. The quantity discounts and license fee mechanisms coordinates and provides winwin opportunities for all the settings and decisions for which it is analyzed.
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3. The revenue sharing, mail-in-rebates, wholesale price discount, and slotting
allowances are the mechanisms which failed to provide coordination or win-win
opportunities or both under certain conditions.
10.3 Implementation issues
In this section, we shall briefly address some managerial concerns on implementing the
contract mechanisms discussed in this dissertation.
1. In the entire study, we have assumed symmetric and complete information among
different SC players. However, symmetric and perfect information is a rare
phenomenon in practice. Business entities are generally reluctant to share their cost
and demand information, as this information can be a source of competitive
advantage. The challenge therefore is to motivate them to share the information less
reluctantly. For example, in situations where information is a source of
competitiveness for a firm or a SC, the player who holds that information can be
sufficiently compensated by providing a greater share of the additional profit (by
appropriate fine tuning of the contract parameters).
2. When the demand is uncertain, if a SC player anticipates a greater risk due to
uncertain demand or supply element, he might be reluctant to sign the contract even
if his expected profits are increasing. One of the possible ways to resolve such a
conflict would be, to compensate that player with a greater share of the additional
profit (again by appropriate fine-tuning of the contract parameters).
3. This study clearly demonstrates the existence of the win-win situations in a multitude
of settings. Often, the win-win opportunities exist for a broad range of values of the
contract parameters. It might be challenging for SC players to negotiate and agree on
to specific value for the contract parameters, since each player would like to have a
greater part of the improved profit. The power of SC players will play a crucial role
in setting the specific value for the contract parameters thus influencing the actual
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CONCLUSIONS AND DIRECTIONS FOR FUTURE RESEARCH
distribution of the enhanced profits. If the power is unbalanced, then the most
powerful player will tend to take away the major share, which will make the less
powerful player less interested in signing the contracts.
4. This study analytically demonstrates that the profit sharing mechanism is as good or
superior to the revenue sharing in enabling coordination and providing win-win
opportunities. However, implementation of the profit sharing mechanism requires
that the Buyer determines his profit unambiguously and share his profit information
truthfully. Unfortunately, this frequently cannot be verified correctly as the profit
figures of most businesses are often disputable. Though the revenue sharing
mechanism has less of this problem, it is not going to be fairly straightforward to
implement either of these mechanisms. Both these mechanisms mandates
investments in information technologies, personal training & time, as the revenue or
the profit figures needs to be communicated and administered regularly. The player
who has to make these investments will be interested in the pay-back period. If the
contract does not provide him the incentives to enable proper compensation, he
would be reluctant to buy in the concept of contract mechanisms.
10.4 Directions for further research
In this section, we provide an overview of some of the directions in which this research
can be extended.
1. Each study in this dissertation can be extended to a multi-echelon (more than two
players) SC setting. More specifically, to design contract mechanisms for
coordinating different operational and marketing decisions in a multi-echelon SC.
2. This study assumes symmetric and perfect information between the Buyer and the
Supplier. Relaxing this assumption can help us estimate the value of information that
each player holds. More importantly, this could help in arriving at a more precise
parameter estimate within the win-win region. This could also pave the way for
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10
designing incentive mechanisms to motivate the SC players for sharing the relevant
information more transparently and truthfully.
3. Considering the competition at different levels of the SC, and designing contracts for
coordination and win-win opportunities will improve the practical relevance of the
current study. Game-theoretic models would be a valuable tool to research in this
direction.
4. In this study, we design coordination mechanisms when the demand is uncertain and
follows a general distribution. Further research can be performed by considering
different levels of uncertainty, such as uncertainty over demand distribution, cost
parameters and willingness-to-pay.
5. This study does not address the effectiveness of contracts in a setting where the
products can be sold in more than one period. Extension of our study in a multiperiod is therefore an interesting possible future extension.
6.
Other decisions that can be considered for further research could be quality of the
product, capacity, and maintenance. Other coordination mechanisms such as quantity
flexibility and capacity reservation contracts can be analyzed in a variety of settings,
especially in the presence of demand and Supply uncertainty.
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Summary in English
Companies can no longer perceive themselves as stand-alone entities in the business
environment. As a result of major trends such as Globalization, Core-business,
Outsourcing and Off-shoring, companies have more-and-more begun to perceive
themselves as part of a chain (or network) of companies. With the increased length of
chains and the increased interdependencies between organizations, coordination between
such entities has become an important managerial challenge. This has led to considerable
interest among both practitioners and academics in the field of Supply Chain
Management (SCM).
In this dissertation SCM is defined as: The coordination of different business entities in
the supply chain to reduce waste (costs) and create value to customers and thus enhance
revenues. Here, coordination refers to managing challenges due to interdependencies
among business entities by aligning goals, processes/functions, decisions, and activities.
One of the most important managerial problems in any Supply Chain (SC) consisting of
autonomous organizations is sub-optimization due to the fact that the SC decision making
is distributed over the various players. In such a setting, so-called contract mechanisms
might be used. Ideally, contract mechanisms ensure that the SC is optimized as if it were
a single unit (coordination) and is designed such that all players benefit from working
together through the coordinating mechanism (win-win). The beauty of contract
mechanisms is that these are designed in such a way that the decision authorities remain
unchanged, but the incentives of the various SC entities are aligned in such a way that
optimizing one’s own situation, “automatically” optimizes the SC.
A SC is said to be coordinated (or optimized) if it achieves the same profit as it would in
a centralized situation (or full partnership). Furthermore, win-win is said to be achieved if
all the players make a greater profit when compared to the decentralized decision making
situation. It is to be noted that one does not imply the other; a coordinated SC might fail
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SUMMARY IN ENGLISH
to provide additional profit to one of the players. Also, even if all players gain from their
collaboration, the SC is not necessarily optimized.
Most of the literature seems to focus on achieving SC coordination while ignoring the
win-win component. However, when the SC consists of autonomous organizations,
clearly, from an implementation point of view, win-win is probably more important than
SC coordination. After all, only if the player will gain from the collaboration will he be
willing to participate in joint actions. Furthermore, since the SC as a whole is nobody’s
specific focus, the optimal SC result can be seen as less important from a practical point
of view.
The dissertation aims to devise incentive/contract mechanisms and contribute to the
understanding of how such mechanisms can coordinate operational and marketing
decisions across autonomous organizations and lead to win-win situations. In this
dissertation, we focus on a range of operational and marketing decisions like pricing and
replenishment, promotions, service-level, and product line. We design and analyze
different contract mechanism which can coordinate each of these decisions in a variety of
SC settings. We make use of simple but theoretically strong models and address the
coordination and the win-win aspect explicitly in each of them. We also establish
relationships between the parameters of different contract mechanisms wherever possible.
Furthermore, we analyze and review the different mechanisms from an implementation
perspective.
The dissertation uses analytical modeling as a tool to design contract mechanisms for
different supply chain structures, selling different product types, and operating under
different demand and supply conditions.
After outlining the problem statement and the conceptual model in Chapter 1 and the
literature review in Chapter 2, the various models are discussed in Chapters 3-9. The
structure of each of these chapters is straightforward. First, the SC structure and decision
authorities of various players in the SC are introduced. In all chapters a two-stage SC
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271
with a Supplier delivering to a Buyer who in turn delivers products/services to customers
is considered. Next, in each chapter it is shown that decentralized decision making leads
to sub-optimal solutions. Subsequently, in each chapter various contract mechanisms are
introduced and tested on their ability to achieve coordination and win-win.
Chapter 3 discusses a basic model with deterministic demand which is a linear function
of price. The decisions to be coordinated are the pricing by the Supplier and Buyer and
the order quantity of the Buyer. It is shown that the contract mechanisms revenue sharing,
profit sharing, quantity discounts and license fee all can lead to coordinated SCs and winwin.
In Chapter 4 we study a model in which the Buyer and Supplier are assumed to have
increasing marginal costs (represented by quadratic functions) and the market price of the
product is fixed. The decisions to be coordinated are the pricing by the Supplier and the
order quantity as determined by the Buyer. It is shown that revenue sharing coordinates
the SC but does not provide win-win. However, it is demonstrated that profit sharing,
quantity discounts and license fee mechanisms can lead to coordination and win-win.
In Chapter 5 we discuss a situation in which the end-consumers are comprised of two
segments. It is assumed that one consumer-segment has a high willingness-to-pay and the
second has a low willingness-to-pay. The decisions that need to be coordinated are the
pricing by the Supplier and Buyer and the order quantity of the Buyer. We design
revenue and profit sharing mechanisms and show that both these mechanisms can
coordinate and provide win-win opportunities for all parameter values.
In Chapter 6 we discuss a model where the end-consumer demand is uncertain. The
decisions to be coordinated are the pricing by the Supplier and the order quantity as
determined by the Buyer. It is shown that the contract mechanisms revenue sharing,
profit sharing, license fee and buy-back contract all can lead to coordinated SC and winwin. We discuss the risk and the reward sharing with each of the contract mechanisms
with the help of a numerical example.
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Chapter 7 discusses a basic model with deterministic demand which is a linear function
of the price. The order quantity decision of the Buyer and the promotion decision of the
Buyer and the Supplier need to be coordinated. It is shown that direct rebates (mail-inrebate) and trade promotion (supplier rebate) do not provide coordination and win-win
opportunities simultaneously. We design a new mechanism called the “combined rebate
mechanism” and show that it can provide both SC coordination and win-win
opportunities.
In Chapter 8, a model is discussed in which the end-consumer demand is influenced by
the price of the product and by the service-level provided at the Buyer’s outlet. Two
different scenarios are considered: one in which the Buyer makes the service-level
decision and the other in which the Supplier makes the service-level decision. In both
scenarios it is assumed that the player who makes the service-level decision also incurs
the cost associated with the chosen service provision. The pricing decisions of the Buyer
and Supplier need to be coordinated and the service-level decision of the player who is
providing the service needs to be coordinated. Four contract mechanisms, namely the
revenue sharing, profit sharing, quantity discount and the license fee mechanism, are
designed in both settings with the following results. The revenue sharing mechanism
coordinates the pricing decision but not the service-level decision for all values of the
cost of service provision. However, win-win opportunities are achieved for the entire
range of the cost of service provision. The profit sharing, quantity discounts and license
fee mechanisms are shown to coordinate the pricing and service-level decisions and also
provide win-win opportunities for the entire range of the cost of service provision.
In Chapter 9 we study a model in which the end-consumers are comprised of two
segments (high willingness-to-pay and low willingness-to-pay) and where the product
variety and the pricing decisions of the Buyer and Supplier need to be coordinated. In the
above setting, it is shown that a decentralized SC can either stocks the same, a lower or
higher number of product variants when compared to a centralized SC. Under certain
conditions the decentralized SC can also have wrong focus whereby it sells single
product to the Highs when a centralized SC would sell a single product to both the
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segments. We design revenue and profit sharing mechanisms and show that coordination
and win-win opportunities are achieved for all parameter values. Moreover, an
equivalence relationship is established between revenue and profit sharing mechanisms.
Finally, in Chapter 10 we draw some general conclusions for each decision and discuss
the performance of different contract mechanisms under different SC settings. We also
provide an overall conclusion based on the central problem statement of this dissertation,
touch upon the implementation issues, and provide directions for further research.
The aim of this dissertation is to present theoretical insights with the possibility for
practical use by SC managers, i.e., to provide academic rigor in combination with
practical relevance. The theoretical contribution and the managerial relevance of the
results obtained in this thesis are summarized below.
Theoretical contribution
1. This study addresses a wide range of decisions at the interface of operations and
marketing in a variety of SC settings. The decisions we address in this thesis are:
(a) pricing and replenishment (b) promotions (c) service-level and (d) product line
decisions. Evidently, Marketing and Operations are to collaborate and align
incentives in any smooth running organization. In this sense, this dissertation can
be considered as a contribution to bridging the gap between the two fields.
2. In all the above decisions, we explicitly address the issue of whether win-win
situations always exist when contracts are used. Literature concerning this issue is
almost nonexistent. This can be seen as a serious omission in the literature,
because, as mentioned, in our opinion win-win is crucial for implementing SC
collaboration and in that sense probably more important than achieving
coordination.
3. We apply a wide range of contract mechanisms and try to identify the
relationships that exist among them. We also discuss these mechanisms from an
implementation perspective.
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4. Varied SC settings have been used and a variety of decisions of significant
practical relevance have been studied. In fact, each model discussed was inspired
by one or two papers from the existing literature. By applying our approach, more
insight and further results are obtained for these well-established models.
Managerial relevance & contribution
1. The decisions that are covered within this thesis (pricing and replenishment,
promotions, service-level or quality, and product line) are very fundamental and
therefore critical to SC managers.
2. This study can help (SC) managers to realize and understand the potential of
contract mechanisms. Purposely we have chosen easy-to-understand models, so
that the results can actually be used as a “convincing tool” for managers. In fact,
over the last years, we have discussed these models, not only at academic
conferences but also at managerial conferences and seminars, and for business
students. These experiences have shown us that indeed our models are useful for
this purpose.
3. When more than one mechanism coordinates and provides win-win scenarios, we
try to identify mechanisms which are easier to implement.
In this flat (globalized) world we are encouraged to believe that incentive alignment will
help businesses to deliver value to their customers and maintain/enhance their
competitive positioning. In our view this thesis will aid businesses align the incentives
within their SC.
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Nederlandse samenvatting
Contractmechanismen voor het Coördineren van Operations en
Marketing Beslissingen in een Supply Chain: Modellen en Analyse
Organisaties kunnen zichzelf niet langer beschouwen als op zichzelf staande entiteiten in
hun bedrijfsomgeving. Als gevolg van belangrijke trends zoals globalisering, het
focussen op de core-business, outsourcing en offshoring, zijn organisaties steeds vaker
een niet los te koppelen onderdeel van een keten (of netwerk) van bedrijven. Vanwege de
toegenomen lengte van ketens en de toegenomen onderlinge afhankelijkheden tussen de
aan elkaar toeleverende organisaties, is coördinatie tussen dergelijke entiteiten een
belangrijke managementtaak geworden. Dit heeft bij zowel managers als wetenschappers
geleid tot een grote interesse in het vakgebied ketenmanagement, oftewel Supply Chain
Management (SCM).
SCM wordt in deze dissertatie gedefinieerd als: “De coördinatie van verschillende
bedrijfsentiteiten in de Supply Chain om op die manier verspilling (kosten) te reduceren
en tegelijkertijd meer klantwaarde te creëren, en zo de opbrengsten te verhogen”. In deze
definitie verwijst “coördinatie” naar de managementuitdaging om –door middel van het
in overeenstemming brengen van doelen, processen, functies, beslissingen en
activiteiten– de verschillende entiteiten binnen de keten op elkaar af te stemmen.
Eén van de belangrijke managementproblemen in een Supply Chain (SC), bestaande uit
autonome organisaties, is de suboptimalisatie die ontstaat doordat de besluitvorming is
verdeeld over verschillende partijen in de keten. Omdat elke entiteit zijn eigen prestaties
centraal stelt, soms ten koste van ketenpartners, worden de optimale prestaties van de
keten als geheel niet bereikt. In een dergelijke situatie kunnen zogenaamde
contractmechanismen worden gebruikt om suboptimalisatie tegen te gaan. Idealiter
zorgen contractmechanismen er voor dat de SC wordt geoptimaliseerd alsof het een
enkele eenheid zou zijn (coördinatie) en worden ze zodanig ontworpen dat alle partijen
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NEDERLANDSE SAMENVATTING
profiteren van de samenwerking door middel van het coördinatiemechanisme (win-win).
Het mooie van contractmechanismen is dat deze worden ontworpen op een manier dat de
besluitvormingsautoriteiten onveranderd blijven, maar dat de incentives van de
verschillende SC entiteiten zodanig op elkaar zijn afgestemd dat men door het
optimaliseren van de eigen situatie “automatisch” ook de SC als geheel geoptimaliseerd.
Een SC heet gecoördineerd (of geoptimaliseerd) als dezelfde winst wordt gegenereerd als
in een gecentraliseerde situatie (ook wel volledig partnership genoemd) waarin alle
beslissingen bij één beslisser liggen. Verder wordt een win-win situatie gerealiseerd als
alle partijen meer winst genereren ten opzichte van de situatie waar alle beslissingen
decentraal worden genomen. Hierbij dient er te worden opgemerkt dat het een niet
automatisch het ander betekent. Het kan zo zijn dat een gecoördineerde SC niet in staat is
om extra winst te verschaffen aan een van de partijen. Tevens is het zo dat, zelfs als alle
partijen profiteren van de samenwerking, de SC niet noodzakelijk geoptimaliseerd is.
De literatuur binnen dit vakgebied lijkt zich te richten op het bereiken van SC coördinatie
waarbij de win-win component grotendeel wordt genegeerd. Echter, vanuit een
implementatieperspectief is win-win waarschijnlijk belangrijker dan SC-coördinatie,
vooral wanneer de SC uit autonome organisaties bestaat. Immers, alleen als een partij
profiteert van samenwerking zal deze bereid zijn te participeren in gezamenlijke acties.
Daarnaast is zo dat –omdat er niemand is de SC als geheel bestuurt en/of daarvoor
verantwoordelijk is– vanuit praktisch perspectief het optimale SC resultaat als minder
relevant kan worden beschouwd.
Deze dissertatie richt zich op het ontwerpen van contractmechanismen en op het
begrijpen
van
hoe
dergelijke
mechanismen
operations-
(logistieke)
en
marketingbeslissingen kunnen coördineren tussen autonome organisaties en kunnen
leiden tot win-win situaties. Het proefschrift richt zich op verschillende operations- en
marketingbeslissingen
zoals
prijsstellingen,
bestelhoeveelheden,
voorraadniveaus,
promoties, serviceniveaus en de breedte van assortimenten (aantal varianten van een
product). In verschillende SC settings worden verschillende contractmechanismen
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NEDERLANDSE SAMENVATTING
ontworpen en geanalyseerd die deze beslissingen kunnen coördineren. Hierbij wordt
gebruik gemaakt van simpele maar theoretisch robuuste modellen. In de analyse van deze
modellen wordt zowel de coördinatie als het win-win aspect benadrukt. Waar mogelijk
worden ook relaties tussen de parameters van verschillende contractmechanismen
geconstrueerd.
Verder
worden
de
verschillende
mechanismen
vanuit
een
implementatieperspectief geanalyseerd.
Met betrekking tot de gebruikte methodologie geldt dat de dissertatie gebruik maakt van
het analytisch modelleren als methode om contractmechanismen te ontwerpen voor
verschillende supply chain structuren en de beslissingen van de verschillende entiteiten
daarbinnen. Als zodanig worden de methodes en technieken van het vakgebied van de
besliskunde (operations research/management science) toegepast.
Na de probleemstelling en het conceptueel model in hoofdstuk 1 en het
literatuuronderzoek in hoofdstuk 2, worden de verschillende modellen besproken in
hoofdstuk 3-9. De structuur van elk van de laatstgenoemde zeven hoofdstukken is als
volgt: Allereerst worden de specifieke SC structuur en de besluitvormingsautoriteiten van
de verschillende partijen in de SC geïntroduceerd. Alle hoofdstukken hebben
gemeenschappelijk dat wordt ingegaan op een SC bestaande uit een toeleverancier
(verder te noemen de “Supplier”) die levert aan een koper (de “Buyer”) die op zijn beurt
weer producten/diensten aan de consument levert. In elk hoofdstuk wordt eerst
aangetoond dat gedecentraliseerde besluitvorming leidt tot suboptimale oplossingen.
Vervolgens worden in elk hoofdstuk een aantal verschillende contractmechanismen
geïntroduceerd die worden getest op hun mogelijkheid om coördinatie en win-win te
bereiken.
Hoofdstuk 3 bespreekt een basismodel waarin de consumentenvraag deterministisch is en
een lineaire functie is van de prijs. De beslissingen die moeten worden gecoördineerd zijn
de prijsstelling door de Supplier en de bestelhoeveelheid van de Buyer. Er wordt
aangetoond dat de contractmechanismen omzetdeling (verder te noemen “revenue
sharing”), winstdeling (profit sharing), kwantumkortingen (quantity discounts) en
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licenties (licence fee) allemaal kunnen leiden tot zowel gecoördineerde SC’s als win-win
situaties.
Hoofdstuk 4 beschouwt een model waarin wordt verondersteld dat de Buyer en de
Supplier beide toenemende marginale kosten hebben (de kosten worden weergeven door
kwadratische functies van de geproduceerde hoeveelheid) en dat de consumentenprijs van
het product door de markt wordt bepaald en dus vast staat. De beslissingen die moeten
worden gecoördineerd zijn de prijsstelling van de Supplier en de bestelhoeveelheid van
de Buyer. Eerst wordt gedemonstreerd dat revenue sharing de SC coördineert maar niet
leidt tot win-win. Vervolgens wordt aangetoond dat de mechanismen profit sharing,
quantity discounts en licence fee wel kunnen leiden tot zowel coördinatie als win-win
situaties.
Hoofdstuk 5 bestudeert een SC waarin de eindgebruikers uit twee segmenten bestaan en
waarbij wordt verondersteld dat het ene eindgebruikersegment een grote bereidheid, en
het andere segment een kleine bereidheid heeft tot betalen. De beslissingen die moeten
worden gecoördineerd zijn de prijsstelling van zowel de Supplier als de Buyer alsmede
de bestelhoeveelheid van de Buyer. De contractmechanismen revenue sharing en profit
sharing worden geanalyseerd en er wordt aangetoond dat beide mechanismen zowel de
SC coördineren als win-win mogelijkheden bieden voor alle mogelijke parameter
waarden.
Hoofdstuk 6 bespreekt een model waarin de vraag van de eindgebruiker onzeker is (dat
wil zeggen, de consumentenvraag wordt door een stochastische verdeling beschreven).
De beslissingen die moeten worden gecoördineerd zijn wederom de prijsstelling van de
Supplier en de bestelhoeveelheid van de Buyer. Voor een dergelijke SC situatie wordt
aangetoond dat de contractmechanismen revenue sharing, profit sharing, licence fee en
buy-back (terugkoop) contracten allemaal kunnen leiden tot zowel een gecoördineerde
SC als win-win. Tevens wordt in dit hoofdstuk aan de hand van een numeriek voorbeeld
verder ingegaan op de verdeling van winst en risico bij elk van de contractmechanismen.
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Hoofdstuk 7 stelt een model aan de orde waarbij de vraag deterministisch is en een
lineaire functie is van de prijs. Binnen dit model dient de beslissing over de bestelgrootte
van de Buyer en de promotiebeslissing van de Buyer en Supplier op elkaar afgestemd te
worden. We laten zien dat het in de praktijk veel gebruikte zogenaamde mail in rebate
(directe kortingen) mechanisme, al dan niet in combinatie met trade-promotie, niet voor
een optimale afstemming zorgt en bovendien geen win-win situatie creëert. In dit
hoofdstuk wordt een nieuw mechanisme genaamd “combined rebate mechanism”
(gecombineerde korting mechanisme) voorgesteld en er wordt aangetoond dat met dit
mechanisme zowel SC coördinatie als een win-win situatie behaald kan worden.
Hoofdstuk 8 bediscussieert een model waarbij de vraag door de eindgebruiker wordt
beïnvloed door de prijs van het product en het niveau van service in de winkel. Twee
verschillende situaties worden besproken. In de eerste situatie wordt een model
beschouwd waarbij de Buyer het serviceniveau bepaalt. In de tweede situatie beslist de
Supplier over het serviceniveau. Bij beide situaties wordt verondersteld dat de beslisser
over het serviceniveau ook de kosten draagt voor het gekozen serviceniveau. Naast de
beslissing over het serviceniveau dient bij beide situaties de beslissing over de prijs door
zowel de Buyer als de Supplier te worden gecoördineerd. In dit hoofdstuk worden vier
contractmechanismen, namelijk revenue sharing, profit sharing, quantity discounts en
licence fee op beide situaties toegepast met de volgende resultaten: Revenue sharing
coördineert niet voor alle kostenniveaus van dienstverlening de prijsbeslissing. Echter,
revenue sharing maakt wel mogelijk dat binnen ieder niveau van de kosten voor de
dienstverlening win-win situaties kunnen ontstaan. De mechanismen profit sharing,
quantity discounts en licence fee coördineren wel zowel de prijsbeslissing als het
serviceniveau en zorgen bovendien voor win-win situaties voor ieder niveau van de
kosten voor de dienstverlening.
Hoofdstuk 9 analyseert een model waarbij de eindgebruikers, evenals in hoofdstuk 5, zijn
ingedeeld in twee segmenten (grote en kleine bereidheid om te betalen). In dit model
dient zowel het aantal productvarianten (breedte van het assortiment) als het vaststellen
van de prijs door zowel de Buyer als de Supplier gecoördineerd te worden. In dit
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hoofdstuk wordt eerst aangetoond dat een gedecentraliseerde SC een lager maar ook een
hoger aantal productvarianten op voorraad kan houden vergeleken met een
gecentraliseerde SC. Het belangrijkste resultaat in dit hoofdstuk is dat voor alle
parameterwaarden zowel revenue sharing als profit sharing zowel de prijsbeslissing als
de assortimentsbeslissing coördineren en kunnen leiden tot win-win. Dit in tegenstelling
tot het in de praktijk veel gebruikte “slotting allowance” mechanisme (waarbij de Buyer
per op voorraad gehouden productvariant een vast bedrag ontvangt) dat slechts voor
bepaalde parameterwaarden leidt tot coördinatie en win-win.
De dissertatie wordt afgerond in hoofdstuk 10. In dat hoofdstuk komen algemene
conclusies, implementatiekwesties en een aantal suggesties voor verder onderzoek aan de
orde.
Het doel van deze dissertatie is om theoretische inzichten te verschaffen met de
mogelijkheid tot praktische toepassing door SC managers om op die manier “academic
rigor” te combineren met “practical relevance”. De theoretische en praktische bijdrage
van dit proefschrift worden hieronder samengevat.
Theoretische bijdrage
1) Deze studie behelst een breed scala aan beslissingen op het snijvlak tussen operations
en marketing in een groot aantal SC situaties. De beslissingen die in dit proefschrift
behandeld worden zijn: (a) vaststellen van de prijs en bestelhoeveelheid; (b)
promoties; (c) niveau van dienstverlening; en (d) assortiment beslissingen. Uiteraard
zullen marketing en operations moeten samenwerken en dus hun incentives moeten
afstemmen om op die manier een soepel werkende organisatie te realiseren. Deze
dissertatie kan dan ook gezien worden als een bijdrage om de kloof tussen deze twee
onderdelen (en vakgebieden) te dichten.
2) In elk van de hierboven beschreven beslissingen komt wanneer er met
contractmechanismen wordt gewerkt de vraag of win-win situaties altijd bestaan
steeds expliciet aan de orde. Opmerkelijk genoeg is er in de literatuur nauwelijks
aandacht voor dit vraagstuk. Dit gebrek aan aandacht kan worden gezien als een
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ernstige tekortkoming, aangezien juist win-win situaties cruciaal zijn om
samenwerking binnen de SC te realiseren en dus waarschijnlijk nog belangrijker zijn
dan het bereiken van SC coördinatie.
3) We passen een breed scala aan contractmechanismen toe en identificeren de relaties
die er tussen de diverse modellen bestaan. We bespreken eveneens hoe deze modellen
geïmplementeerd kunnen worden.
4) Er zijn verschillende SC situaties gebruikt en er is een breed scala aan praktisch
relevante beslissingen bestudeerd. In feite zijn alle modellen die in de dissertatie
besproken worden, ieder gebaseerd op een of twee specifieke studies uit de literatuur.
Door de in dit proefschrift gekozen aanpak wordt niet alleen meer inzicht, maar zijn
ook verdere resultaten, verkregen voor deze uit de literatuur bekende modellen.
Relevantie voor, en bijdrage aan, management
1) De beslissingen die behandeld worden (zoals prijsbeleid, bestelhoeveelheden,
promotie, serviceniveau en de breedte van het assortiment) behoren tot de
fundamentele beslissingen binnen marketing en operations en zijn daarom van groot
belang voor SC managers. Dit onderzoek kan er toe bijdragen dat (SC) managers de
mogelijkheden van de verschillende contractmechanismen beter begrijpen, waarmee
de bereidheid om deze ook toe te passen wordt gestimuleerd. Met opzet is in dit
proefschrift gekozen voor modellen die relatief eenvoudig te begrijpen zijn. Dit heeft
als groot voordeel dat de resultaten gebruikt kunnen worden om managers te
overtuigen. We hebben deze modellen de afgelopen jaren niet alleen op academische
congressen bediscussieerd, maar ook op bijeenkomsten voor managers en
bedrijfskundestudenten. Op basis van deze ervaringen zijn we tot de conclusie
gekomen dat deze modellen inderdaad bruikbaar zijn voor een beter begrip van, en
waardering voor, contractmechanismen.
2) In die gevallen waar meerdere modellen voor win-win situaties zorgen, geven we aan
welk model het eenvoudigst toe te passen is.
In deze platte (geglobaliseerde) wereld worden we aangemoedigd om te geloven dat het
afstemmen van incentives het bedrijfsleven helpt om waarde te creëren voor de klanten
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en hun positie te handhaven en verstevigen. Hopelijk zal dit proefschrift hieraan een
bijdrage leveren door het bedrijfsleven te stimuleren de incentives binnen de SC beter op
elkaar af te stemmen.
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Curriculum vitae
Vijayender Reddy Nalla holds an MS in Industrial Management from the Indian Institute
of Technology (IIT), Madras, India and a Bachelors in Mechanical Engineering. He
joined the cluster for Marketing and Supply Chain Management at Nyenrode Business
universiteit in September 2002. He is working as a researcher in the center ever since,
and started working on his PhD shortly after that. His research interests are focused on
Supply Chain Management, Operations Management and Modeling Business Decisions.
His PhD research is focused on designing mechanisms which would coordinate the
Operational & Marketing decisions in a Supply Chain. He is promoted by Prof. Dr.
Venugopal & Prof. Dr. Jack van der Veen. He will continue working for Nyenrode as an
Assistant Professor, and will continue his research on Supply Chain coordination.
His research has been published in the International Journal of Production Research. He
has published his PhD work in several international conferences of POMS, EurOMA &
in the Nyenrode working paper series. Soon after his PhD defense he make full efforts to
publish his research in several international journals.
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