Download The Role of Options in Managing Demand Uncertainty

Derivatives in Supply Chain
Dailun Shi & William Grey
IBM T. J. Watson Research Center
Richard Daniels
University of Georgia
Agenda




Background and Motivation
Research Content
Results
Future Research Directions
Risk Management in The financial
Services Industry






Portfolio management
CAPM
VAR for market and credit risk
Credit rating/scoring methodologies
Options pricing models
Derivative products
Futures, swaps, options, floors, caps, etc.
 Operational risk management techniques
 Risk-adjusted capital allocation
Supply Chain Risk Management
Research at IBM T. J. Watson Center




Supply chain risk profiling
Quantifying financial impacts of risks
Risk assessment
Risk management strategy - design and
implementation
 Operational management
 Financial management


Insurance products
Options, Futures, Swaps
Derivatives in Supply Chain
 Is there a need for options to manage supply
chain risk?
 Implications of introducing options into SCM:




Behavioral
Financial
Information sharing
Risk sharing
Problem Setting and Parameters
 A single period two-party supply chain:
Supplier
Retailer
End Customers
 Highly perishable, short-life-cycle product
 Two replenishment modes: firm orders & options
 Parameters:





D: stochastic demand with pdf f(D) and cdf F(D)
W: wholesale price = unit cost of firm order
C: unit cost of option, X: option exercise price
R: product retail price, M: unit manufacturing cost
P: penalty for defaulting on options
 expediting cost vs. cash penalty
The Newsvendor Problem
 Overage risks of salvaging
inventory at loss
 Price markdowns
 Inventory holding costs
 Underage risks of unmet
demand
 Lost profit
 Cost of expediting
 Customer ill will
 Implications for the retailer
 Order less than in ISC
 Bear all overage risks
 Has some underage risks
 Implications for the supplier
 Build to order
 No overage risks
 Substantial underage risks
Feasibility Conditions
 Following conditions hold among parameters
M < W < C+X < R
PM
X>S
 Those conditions ensure well-behaved profit
functions, thus lead to unique optimal
solutions
Sequence of Events
Background: procurement decisions is made before selling season, with no
opportunity to replenish inventory once the season starts
 Transaction terms (W, C, X, P) are determined
 At t=0
The retailer places orders Q and q
The supplier decides production quantity Y
The supplier delivers Q units, holds (Y-Q) inventory
 During the season t1
The retailer exercises options ( q)
The supplier delivers additional units to the retailer
The Retailer’s Decisions
 The retailer has two decision variables: number
of firm orders Q and number of options q.
 Total order quantity T = Q+q
 The retailer’s expected profit function:
Q
T
0
Q
E (Q, T )  ( X  C  W )Q  ( R  X  C )T  ( R  S )  F ( D)dD  ( R  X )  F ( D)dD
 The retailer’s optimal order quantities:
F (T *)  Pr( D  T *) 
R X C
RX
F (Q*)  Pr( D  Q*) 
X  C W
X S
The Supplier’s Decisions
 Decision variable for the supplier: Y = the number of
products to produce, and its range is Q*Y T*
 The supplier’s expected profit function:
E(Y )  (W  P)Q * ( X  C  P)q * ( P  M )Y
Y
T*
 ( X  S )  F ( D)dD  ( X  P) 
Q*
Y
F ( D)dD
 The unique maximum point of the expected profit function:
F (Y * *)  Pr( D  Y * *) 
PM
PS
 The supplier’s optimal production quantity Y*:
Q*,

Y *  Y * *,
T *,

if Y * *  Q *
if Q*  Y * *  T *
if T *  Y * *
Results
 Supply Chain Coordination
 Risk Sharing
 Information Sharing
 Supply Chain Contract Negotiation
Supply Chain Coordination
 Double Marginality Problem
 Separate ownership of two supply chain parties
 Neither has control of the entire supply chain
 Conflicting objectives
 Asymmetric information about demands
 Total supply chain profit is (R-M)Q, if Q is produced
R W
Q*  F (
)
 Without options, total product quantity:
RS
RM
 Integrated supply chain produces: Q  F ( R  S )
 Since M < W, Q *  QI*
1
*
I
1
Supply Chain Coordination (cont..)
 Options introduce three more degrees of
freedom (X, C and P), in addition to W
 Conditions for the retailer to coordinate:
R X C R M

 T *  Q * q*  QI*
RX
RS
 Conditions for the supplier to coordinate:
PM R X C

 Y*  T *
PS
RX
Risk Sharing
 Options provide a tool for the retailer to
manage demand uncertainty
Firm orders for demand relatively sure to sell
Options for products less likely to be needed
Hedge against both overage and underage risks
Pay a premium to purchase options
 Options also benefit the supplier
Inducing the retailer to purchase more products
Must hold inventories for options
 Bottom-line: both parties are better off
Risk Sharing (cont.)
Profit Increase
Profits Improvement from Options
90.0%
manufacturer (mean = 3000)
80.0%
retailer (mean = 3000)
Chain (mean =300)
70.0%
manufacturer (mean = 4000)
retailer (mean = 4000)
60.0%
Chain (mean =4000)
50.0%
40.0%
30.0%
20.0%
10.0%
0.0%
0
400
800
1200
1600
demand stdv
2000
Risk Sharing (cont.)
 Two fundamental issues in supply chan optimization with options:
 Set transaction parameters to maximize total profits
 Allocate total profit equitably between the two parties
 Observations:
 Coordination conditions ensure profits of ISC
 Coordination conditions provide no insight into total profit allocation
 Wholesale price W is not in the coordination conditions
 W doesn’t effect T* and Y*
 Varying W is effective for total profit allocation
 Two potential ways for the profit allocation:
 Set X, C, P, and W to ensure both parties better off
 Distribute profit based on “risk-adjusted profit”
Information Sharing
 Fix contract terms (R, W, X, C, P and M), RHS of equations
for T*, Q*, Y** are constant, denoting them CT*, CQ*, CY**
 Assume normal demand with mean µ and stdv σ, we have:
Z     1 (C Z ) for Z = T*, Q*, and Y**
1
1
q *  (CT * )   (CQ* )

T*
 /    1 (CT * )
 The implied θ in Y* = Q* + θq* is constant w.r.t to µ and σ


 The above results are also true for non-normal demand
 Information implications of the 3rd result:
 The retailer’s (Q*, q*) reveal demand information (µ,σ) completely
 The supplier always produces fixed percentage for options
Supply Chain Contract Negotiation
 Contract terms and conditions are usually determined by:
 Relative market power
 Incentive considerations
 Promotions
 Understanding the impacts of contract parameters (R, X, C,
W, P) on both parties’ profits is important
 We have analytic results on related questions
 The following slides show graphic presentations
Impact of Option Cost C on Profits
profit Increase
35.0%
manufacturer's gain
30.0%
retailer's gain
supply chain gain
25.0%
20.0%
15.0%
10.0%
5.0%
0.0%
10
12
14
16
18
20
22
24
Option Cost C
-5.0%
-10.0%
26
28
Profit Increase
Impact of Exercise Price X on Profits
28.0%
manufacturer's gain
retailer's gain
supply chain gain
24.0%
20.0%
16.0%
12.0%
8.0%
4.0%
0.0%
55
60
65
70
75
option exercise price X
-4.0%
80
Profits
Impact of Wholesale Price W on Profits
Manufacturer
138000
Retailer
Total
123000
108000
93000
78000
63000
48000
33000
18000
3000
40
45
50
55
60
Wholesale Price W
65
% gain of Profits
Impact of Penalty Cost P on Profits
27.0%
manufacturer's gain
retailer's gain
supply chain gain
24.0%
21.0%
18.0%
15.0%
12.0%
9.0%
6.0%
3.0%
40
45
50
55
60
65
70
75
80
85
90
95
penalty cost P
100
Product Availability Insurance
Cost C and Insurance Income
Insurance Income
14000
12000
10000
Insurance Income
8000
6000
4000
2000
Insurance Cost C
0
0
5
10
15
20
Impact of Costs C on Profits
% gain of profit
54.0%
45.0%
36.0%
manufacturer's gain
retailer's gain
supply chain gain
27.0%
18.0%
9.0%
0.0%
-9.0%
-18.0%
0
5
10
15
insurance cost c
20
Future Research Directions
 Supply chain option pricing
 Expand the framework to consider:
Multiple periods
Multiple suppliers
Multiple buyers
 Issues associated with creating markets
to trade supply chain options