Download Research on Service Capacity Coordination Strategy in Product Servitization

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Research on Service Capacity Coordination Strategy in Product
Servitization Supply Chain
YAO Shujun1, 2, CHEN Juhong1
1. School of Economic and Management, Xi’an University of Technology, Xi’an, China, 710054
2. School of Management, Xi’an University of Finance & Economics, Xi’an, China, 710100
Abstract: This paper introduces a three-echelon product Service-oriented supply chain consisting of
specialized service function provider, service integrator and customer. Service integrator purchases
service capacity from specialized service function provider and sales the added service to customer
facing with a price sensitive stochastic demand market. The purpose of service integrator is to meet
expected profit maximization through the optimal service capacity order quantity and price of integrated
services. Specialized functions service provider identifies the best service capacity price to maximize the
expected profit. Establishing the revenue model and supply chain coordination model in product
Service-oriented supply chain based on service capacity. Through the numerical example, we find that
service capability has an important influence on product Service-oriented supply chain coordination
performance.
Keywords: Service outsourcing, service capacity, Stochastic service demand, supply chain
Classification number: F270.5
Cultural heritage marking code: A
1 Introduction
The definition of supply chain in domestic and foreign literatures concentrated on logistics flow,
information flow and capital flow in the process from the raw material supply to final product delivery,
ignoring service elements in the supply chain[1]. "Service oriented product supply chain" is the earliest
proposed by Johnsonetal in 2008[2].
In the product service oriented supply chain, service integrators accept various customer service
requirements, design these service requirements, and outsource every well designed service package to
professional function provider. After completion of service processing, the service integrators synthetize
the completed service packages and provide a customized, integrated solutions for customer with
product and service.
The recent literatures dedicated to the study of supply chain management coordinate strategy.
Chenetal[4] believed that reduce the supply chain cost, optimize the structure of incentive to improve
supply chain members of the cooperation between enterprises, improving the overall performance of the
[5]
firstly put forward the service level, but not explicitly considered the capacity
supply chain. Weng
loss cost. However, this paper focuses on the price sensitivity of stochastic demand situation, Service
integrator determines reasonable service provider, function service provider determines reasonable
service ability price. When the service integrator does not undertake service capacity surplus and
insufficient risk, function service provider can design product servitization supply chain coordination
mechanism by effectively control service capacity.
2 Product Servitization Supply Chain Structure Model
We use a state model to research the product servitization supply chain. In this structure model, function
service provider has w units service capacities. The service integrator purchases Q service capacities
from function service provider, and sales the integrated value-added service capacities to customers in
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the market with unit price p . Product servitization supply chain model shown in figure 1:
Fig.1 Three-echelon product Servitization supply chain model
Service integrator faces a price sensitive and stochastic service demand market, with random service
demand function f x ( x | p) , which means probability distribution that service demand along with the
，
service demand price changes. The linear demand relationship between service demand and price for:
x( p) = d − α p
（1）
d α >0
Equation (1) describes the maximum potential market standard of the linear service demand curve: d .
Price sensitive coefficient α .
x( p) ∈  x ( p ) − b, x ( p) + b  belongs to uniform distribution. b is the service demand range
parameter.
Based on the probability distribution of price stochastic demand: f x ( x | p) , the expected profit of
service integrator is :
SIP(P, Q) = ∫
Q
[( p − w)x] f x ( x | p)dX + ∫ Qx( p)+b[( p − w)Q] f x (x | p)dx
x( p )
（2）
The former of equation (2) is expected profit as service demand is less than service capacity. The latter
is expected profit as service demand is more than service capacity.
The expected profit of function service provider is equal to service capabilities Q multiplies service
capacity unit price w .
The capacity cost structure of function service provider consists of service capacity unit cost c and
Scale economic cost
e.
Parameter c is service capacity cost when scale economy is constant
Parameter e is capacity management cost caused by Scale economic infrastructure
expected profit of function service provider can be defined as:
[6][11]
[10]
.
. So the
（3）
FSP(Q ) = wQ − (cQ + eQ 2 ).
Problems faced by service integrator are how many service capacities should be purchased from
function service provider ( Q ) and with what kind of service integrated capacity price to control
customer market ( p ). But the objective of function service provider is to setting an optimal service unit
price ( w ) for service integrator so that achieving maximum expected profit.
Service demand is stochastic, causing function service provider has service capacity surplus and service
capacity insufficient two situations, thus leading to service capacity surplus cost ( SC( p, Q ) ) and
service capacity insufficient cost ( IC( p, Q ) ).
SC( p, Q ) = ∫ Qx ( p ) −b [( w − r )(Q − x)] f x ( x | p )dx
（4）
（5）
IC( p, Q) = ∫ Qx ( p )+b k ( x − Q ) f x ( x | p )dx
Where the parameter r represents the salvage value of service capacity surplus, and the parameter k is
the “opportunity cost” of lost sales due to service capacity insufficient.
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In the product servitization supply chain, the service integrator is close to the market and easy to collect
service demand information and service capacity information of function service provider, effectively
choose appropriate function service provider for cooperation, determines a reasonable price of
integrated service capacity for the end customer ( p ). By adjusting service capacity Q , function service
provider coordinates and controls the entire product servitization supply chain, and undertakes risk cost
under the circumstance of service capacity surplus and service capacity insufficient.
3 Product Servitization Supply Chain Coordination Mechanism
In these circumstances, assuming a core service-oriented enterprise from joint decision-making
perspective between function service providers and service integrator, realize performance optimization
of the entire product servitization supply chain. Therefore, the total expected profit of product
servitization supply chain is the expected profit of function service provider and service integrator minus
service capacity surplus cost ( SC( p, Q ) ) and service capacity insufficient cost ( IC( p, Q ) ):
R1 ( p, Q ) = SIP( p, Q) + FSP(Q) − SC( p, Q) − IC( p, Q) (6)
Where SIP( p, Q) FSP(Q ) SC( p, Q ) IC( p, Q ) have been defined in equation 2
，
，
，
（ ），（ ），（ ）
3
4 .
In the price sensitive stochastic demand conditions of uniform distribution, the total expected profit of
product servitization supply chain equivalence in:
− p − 4be + r − k
)
4b
Q(( p + k )(d − ∂p + b) − 2bc − r (d − ∂p − b))
+
2b
2
( r − p)(d − ∂p − b) k (d − ∂p + b) 2
+
−
4b
4b
R 1 ( p, Q ) = Q 2 (
(7)
When the price of integrated service is greater than the salvage value of unused capacity (p > r) and the
range parameter b is bounded above, it can be shown in Lemma1 that the objective function in equation
(10) is strictly jointly concave, thereby ensuring the existence of a unique optimal solution.
The optimal solution of integrated service price made by service integrator is:
p* =
2α ( r − k ) + 3b
2α − k − 2
（
）
The optimal solution of service capacity made by function service provider:
Q* =
d (2α − k − 2) + b 2α − k +1 +α(2α − k − 2 − 4α2 ) ( r − k )
2α − k − 2
4 Numerical Example Analysis
This section is a numerical analysis of products, mainly research how price sensitive coefficient α and
service capacity unit cost c affect performance of the whole supply service products, and use the
statistical analysis table to illustrate.
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Table 1 Benchmark parameter table
parameter
Benchmark
：d
：α
Zero-price expected demand
100
Price sensitivity parameter
2
：b
Range parameter of uniform distribution
Service capacity unit price c
：
Diseconomy scale parameter： e
：r
Salvage value of per unit over capacity
20
0.5
0.1
5
：k
Opportunity cost of lost sale due to under capacity
8
Table 2 The key parameters affect numerical
：α
1.5
1.6
1.7
1.8
： R 1258.9 1245.5 1145.7 1088．2
SCUP： c
0.1
0.2
0.3
0.4
PSSC-TP： R
1098.5 1032.6 986.56
932.4
PSP：Price sensitivity parameter： α
SCUP：Service capacity unit price： c
PSSC-TP：product servitization supply chain-total profit
PSP
PSSC-TP
∗
1
∗
1
1.9
2
1012.6
987.6
0.5
0.6
894.21
856.6
Fig.2 Price sensitivity affect supply chain performance
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Fig.3 Service capacity affect supply chain performance
5
Conclusion
A three-echelon product Service-oriented supply chain consisting of specialized service function
provider, service integrator and customer has been studied in this paper. Service integrator purchases
service capacity from specialized service function provider and sales the added service to customer, who
is faced with a price sensitive stochastic demand market. The purpose of service integrator is to meet
expected profit maximization through the optimal service capacity order quantity and price of integrated
services. Specialized functions service provider identifies the best service capacity price to maximize the
expected profit. Establishing the revenue model and supply chain coordination mechanism model in
product Service-oriented supply chain based on service capacity.
Through numerical example study in this paper, we find:
First, in the process of constructing product servitization supply chain coordination mechanism, We will
realize maximization of whole supply chain performance, as multiple nodes enterprise competitive
strategy are consistent.
Second, Compared to other nodes enterprise, the enterprise can obtain higher returns from product
servitization supply chain coordination of service products.
However, this model has the following limitations:
First, this paper merely study a harmonious relationship between service integrator and function service
provider, without considering the reality of life and a pair of among them for more than coordinating
relations.
Second, the price sensitivity service demand just follows uniform distribution in our model. In the future,
we should relax restrictions on service products, further study of supply chain coordination strategy.
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