Heavy Traffic Analysis of a Simple Closed Loop Supply Chain

We consider a closed loop supply chain where new products are produced to order and returned products are refurbished for reselling. The solution to a price-setting problem enforces the “heavy traffic” condition, under which we address the production rate control problem for two types of cost functions. We solve a drift-control problem for an approximate system driven by a correlated two-dimensional Brownian motion. The solutions to this system are then used to obtain asymptotically optimal control policies. We also conduct a numerical study to explore the effects of different parameters on the optimal production rates and the resulting costs. MSC2000 Subject Classification: Primary: 60K25, 60K20, 93E20; Secondary: 60K10, 60K30. OR/MS subject classification: Primary: Queues Diffusion Models, Queues Limit Theorems, Queues Networks, Queues Optimization; Secondary: Inventory/Production Policies Marketing/pricing. Running Title: Heavy Traffic Analysis of Closed Loop Supply Chain ∗Department of Statistics, Iowa State University, Ames, IA 50011 †Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011 ‡Corresponding author. E-mail: [email protected], Phone: (515) 294 4347 §Department of Industrial and Manufacturing Systems Engineering, Iowa State University, Ames, IA 50011 ¶Department of Mathematics, Iowa State University, Ames, IA 50011 1