Transcript No Slide Title

RESEARCH TEAM
INVESTIGATORS
R.E. King
S-C. Fang
J.A. Joines
H.L.W. Nuttle
Industrial Engineering
Industrial Engineering
Textile Engineering, Chem. and Science
Industrial Engineering
STUDENTS
P. Yuan
Y. Dai
Y. Ding
MR. Industrial Engineering
Ph.D. Industrial Engineering
Ph.D. Industrial Engineering
OBJECTIVES
• Develop models and tools to support
collaborative efforts in a B2B environment
• Investigate DEA and cooperative game
theory for partnership formation and contract
negotiation
• Incorporate vagueness and uncertainty
through the use of Fuzzy Mathematics
DEA
DATA ENVELOPMENT ANALYSIS

A technique to evaluate the efficiency of business units
performing similar functions.

DEA evaluates business units based on the ratio of weighted
sum of outputs to weighted sum of inputs.

DEA employs a frontier methodology utilizing linear
programming.

Example: collaborative partner selection
• Inputs: unit cost, logistics cost
• Outputs: leadtime, quality, reliability, capacity
Fuzzy DEA
METHODOLOGY

Incorporates vagueness and uncertainty of the qualitative
linguistic terms and measures in business decision
making by using of fuzzy mathematics, e.g., “high” unit
cost, “long” leadtime
• Integrates fuzzy modeling and possibility theory with
traditional DEA analysis. Employs fuzzy linear
programming
• Issue: Fuzzy Linear Programs (FLP) are not well-defined
due to the ambiguity in the ranking of fuzzy sets.
Fuzzy DEA
APPROACHES

a -level based approach
• FLP solved by a parametric programming method based on
different alpha levels
• Based on decision maker’s preference, there are four
models: Best-Best, Best-Worst, Worst-Best, Worst-Worst
•
Possibility approach
• FLP transformed into well-defined possibility DEA
model by using of possibility measures in possibility
theory
• Possibility programming approaches from optimistic
and pessimistic points of view
DEA
APPROACHES (continued)
•
Credibility approach
• FLP transformed into well-defined credibility
programming models by replacing fuzzy variables with
“expected credits” expressed in terms of credibility
measures
• Credibility programming model
DEA
FUZZY DEA SOFTWARE
Prototype Implementation
• Parameter Specification
• Input & output data
• Membership functions
• Data Evaluation
• Efficiency measure calculation
• Output
• Detailed efficiency measure report
DEA
PARAMETER SPECIFICATION
DEA
PARAMETER SPECIFICATION (Graph)
DEA
PARAMETER SPECIFICATION (Spreadsheet)
DEA
DATA EVALUATION AND OUTPUT
For collaborative partner selection
• ABC Textiles, FABRICO, and Sharp Mills are
eliminated since their efficiency is less than one.
• COMFAB and FINETEX are the efficient partners.
Further analysis is needed to distinguish between them.
Game Theoretic Approach to Supply Chain
Management

What is game theory?
 Analysis of situations involving conflicting interests.

Why game theory?
 A softgoods supply chain involves the activity and
interaction of many “players”, each of whom is usually more
interested in maximizing their own profits rather than those
of the supply chain as a whole.

Applications
• Channel Coordination
• Revenue Management
• Capacity Allocation with Multiple Demand Classes
Channel Coordination
N Retailer Capacity Allocation Problem with Market Search
• Capacity allocation problem
When the total order from the retailers exceeds the supplier's capacity, the
supplier needs to allocate his/her supply according to allocation rules.
• Market search
Customers, whose demand cannot be satisfied by one retailer due to
stockout, may visit another retailer.
• Questions
How should the retailers place orders?
How to maximize the performance of the entire supply chain?
Channel Coordination
• Decentralized system
• Players act to maximize their individual profit.
• Use Game theory to find an equilibrium solution.
• Centralized system
• Entire supply chain behaves as if it is owned by one company.
• Find solution that maximizes the total expected profit.
• Channel coordination
• Modify the players' parameters (e.g., wholesale prices) to make
the decentralized equilibrium solution achieve the total expected
profit of the centralized system.
Channel Coordination
Decentralized Control
yd
yk
Supplier
Product : Levis 550
Single period
Dillards
Consumers
Demand Dj
Lost sales
Kohls
yj
JC Penny
ym
Macy’s
Transfer
Demand from
JC Penny to
Macy’s
Consumers
Demand Dm
yh
JC Penny
Hecht’s
Transfer
Demand
from
Macy’s to
JC Penny
Macy’s
Lost sales
Channel Coordination
Centralized Control
Product : Levis 550
Single period
yd
yk
Dillards
Kohls
Consumers
Demand Dj
Lost sales
JC Penny
Supplier
yj
ym
JC Penny
Transfer
Demand from
JC Penny to
Macy’s
Macy’s
Consumers
Demand Dm
yh
Transfer
Demand from
Macy’s to JC
Penny
Hecht’s
Lost sales
Macy’s
Channel Coordination
Model Outputs
•Wholesale prices
• Equilibrium inventory
• Equilibrium profits
Channel Coordination
Example
Decentralized
System
(Before Channel Coordination)
Retailer 1
Retailer 2
Wholesale
Prices
2.00
2.00
Equilibrium
Inventory
65.67
76.50
142.16
66.45
77.82
Equilibrium
Profit
162.83
260.96
142.15
180.23
294.10
System Profit
565.95
Supplier
Decentralized
System
(After Channel Coordination)
Centralized
System
Retailer 1
Retailer 2
710.95
Supplier
Retailer 1
Retailer 2
1.71
1.52
144.27
66.45
77.82
144.27
236.62
180.23
294.10
236.62
710.95
Supplier
Pricing Game in Revenue Management
• Consider multiple firms competing for the
same pool of customers
• Each firm faces random customer demand
• Each firm makes a pricing decision to
maximize their revenue from finite capacity
• For example, yarn suppliers competing to
supply fabric manufacturers
Pricing Game in Revenue Management
Yarn supplier 1
c1 , w1 p1
d1 ( p1 ,..., pn )
. . .
Yarn supplier n
cn , wn pn
Notation for supplier i, i =1,…,n
ci : capacity
pi : selling price
p i ( p1 ,.., pn ) : revenue function
d n ( p1 ,..., pn )
w1 : unit cost of capacity used
di ( p1 ,..., pn ) : demand
Pricing Game in Revenue Management
Results
• Deterministic demand
•Nash equilibrium exists and is unique
•Explicit equilibrium point can be calculated
• Stochastic demand
•Nash equilibrium exists and is unique
•Sensitivity analysis can be done to see the impact of
small change in parameters on Nash equilibrium
Capacity Allocation
with Multiple Demand Classes
Local store
Firm 1
Online store
Online store
Firm 2
Local store
Capacity Allocation with Multiple
Demand Classes
• Case 1: one-period model in which each firm decides its total
capacity
• Nash equilibrium solution exists
• Sensitivity analysis for the equilibrium solution
• Case 2: One-period model in which each firm decides total
capacity and capacity allocation simultaneously
• Nash equilibrium solution exists
• Case 3: Multiple-period model in which each firm decides
total capacity and capacity allocation simultaneously
• Myopic equilibrium is the Nash equilibrium
What’s Next ?
•
Expand research on cooperative games for partnership
formation and contract negotiation
•
Develop on-line versions of the prototype software to
allow on-line access
•
Investigate new tools for collaborative forecasting,
planning, and supply chain inventory management
•
Test these new tools utilizing data from a real softgoods
supply chain