The Role of Options in Managing Demand Uncertainty
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Transcript 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
PM
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 t1
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
RX
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 * *)
PM
PS
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:
RS
RM
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 RM
T * Q * q* QI*
RX
RS
Conditions for the supplier to coordinate:
PM R X C
Y* T *
PS
RX
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