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INVESTIGATORS
R.E. KingS-C. FangJ.A. JoinesH.L.W. Nuttle
STUDENTSP. YuanY. DaiY. Ding
Industrial EngineeringIndustrial EngineeringTextile Engineering, Chem. and ScienceIndustrial Engineering
MR. Industrial EngineeringPh.D. Industrial EngineeringPh.D. Industrial Engineering
RESEARCH TEAM
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.
-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
Fuzzy DEA APPROACHES
• 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
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
Macy’s
Consumers Demand Dj
Consumers Demand Dm
Lost sales
Transfer Demand from Macy’s to JC Penny
JC Penny
Supplier
Dillards
Kohls
Hecht’syh
yd
yk
yj
ym
JC Penny
Macy’s
Decentralized Control Product : Levis 550
Single period
Lost sales
Transfer Demand from JC Penny to Macy’s
Channel Coordination
JC Penny
Consumers Demand Dj
Consumers Demand Dm
Transfer Demand from JC Penny to Macy’s Transfer
Demand from Macy’s to JC Penny
Macy’s
Supplier
Dillards
Kohls
JC Penny
Macy’s
Hecht’syh
yd
yk
yj
ym
Centralized Control Product : Levis 550
Single period
Lost sales
Lost sales
DecentralizedSystem
(Before Channel Coordination)Centralized
System
DecentralizedSystem
(After Channel Coordination)
Retailer 1 Retailer 2 Supplier Retailer 1 Retailer 2 Supplier Retailer 1 Retailer 2 Supplier
WholesalePrices
2.00 2.00 1.71 1.52
Equilibrium Inventory
65.67 76.50 142.16 66.45 77.82 144.27 66.45 77.82 144.27
Equilibrium Profit
162.83 260.96 142.15 180.23 294.10 236.62 180.23 294.10 236.62
System Profit 565.95 710.95 710.95
Example
Channel Coordination
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
Yarn supplier n
Yarn supplier 1
. . .
1 1,c w
,n nc w
1p
np
),...,( 11 nppd
),...,( 1 nn ppd
Notation for supplier i, i =1,…,n capacity unit cost of capacity used selling price demand revenue function
:ic:ip
1 :w1( ,..., ) :i nd p p
:),..,( 1 ni pp
Pricing Game in Revenue Management
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
Firm 1
Firm 2
Local store
Online store
Online store
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