RESEARCH TEAM

1. RESEARCH TEAM Industrial Engineering Industrial Engineering Textile Engineering, Chem. and Science Industrial Engineering INVESTIGATORS R.E. King S-C. Fang J.A. Joines H.L.W. Nuttle STUDENTS P. Yuan Y. Dai Y. Ding MR. Industrial Engineering Ph.D. Industrial Engineering Ph.D. Industrial Engineering

2. 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

3. DEADATA 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

4. 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.

5. Fuzzy DEAAPPROACHES • 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

6. DEAAPPROACHES (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

7. DEAFUZZY DEA SOFTWARE • Prototype Implementation • Parameter Specification • Input & output data • Membership functions • Data Evaluation • Efficiency measure calculation • Output • Detailed efficiency measure report

8. DEAPARAMETER SPECIFICATION

9. DEAPARAMETER SPECIFICATION (Graph)

10. DEAPARAMETER SPECIFICATION (Spreadsheet)

11. DEADATA 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.

12. 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

13. 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?

14. 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.

15. Channel Coordination Decentralized Control Product : Levis 550 Single period yd Dillards Consumers Demand Dj Lost sales JCPenny yk Kohls Transfer Demand from JC Penny to Macy’s yj Supplier JC Penny Transfer Demand from Macy’s to JC Penny ym Macy’s Consumers Demand Dm Lost sales Macy’s yh Hecht’s

16. Channel Coordination Centralized Control Product : Levis 550 Single period yd Dillards Consumers Demand Dj yk Kohls Lost sales JC Penny Transfer Demand from JC Penny to Macy’s yj Supplier JC Penny Transfer Demand from Macy’s to JC Penny ym Macy’s Consumers Demand Dm Lost sales Macy’s yh Hecht’s

17. Channel Coordination Model Outputs • Wholesale prices • Equilibrium inventory • Equilibrium profits

18. Decentralized System (Before Channel Coordination) Centralized System Decentralized System (After Channel Coordination) Retailer 1 Retailer 2 Supplier Retailer 1 Retailer 2 Supplier Retailer 1 Retailer 2 Supplier Wholesale Prices 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 Channel Coordination Example

19. 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

20. Notation for supplier i, i =1,…,n capacity unit cost of capacity used selling price demand revenue function Pricing Game in Revenue Management Yarn supplier 1 . . . Yarn supplier n

21. 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

22. Capacity Allocation with Multiple Demand Classes Local store Firm 1 Online store Online store Firm 2 Local store

23. 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 equilibriumis the Nash equilibrium

24. 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