INVESTIGATORS R.E. King S-C. Fang J.A. Joines H.L.W. Nuttle STUDENTS P. Yuan Y. Dai Y. Ding Industrial Engineering Textile Engineering, Chem. and Science Industrial Engineering MR. Industrial Engineering Ph.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 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 Macy’s Consumers Demand D j Consumers Demand D m Lost sales Transfer Demand from Macy’s to JC Penny JC Penny Supplier Dillards Kohls Hecht’s yhyh ydyd ykyk yjyj ymym 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 D j Consumers Demand D m 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’syhyh ydyd ykyk yjyj ymym Centralized Control Product : Levis 550 Single period Lost sales

Channel Coordination Wholesale prices Equilibrium inventory Equilibrium profits Model Outputs

Decentralized System (Before Channel Coordination) Centralized System Decentralized System (After Channel Coordination) Retailer 1Retailer 2SupplierRetailer 1Retailer 2SupplierRetailer 1Retailer 2Supplier Wholesale Prices Equilibrium Inventory Equilibrium Profit System Profit 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... Notation for supplier i, i =1,…,n capacity unit cost of capacity used selling price demand revenue function 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 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