Heavy Traffic Analysis of a Simple Closed-Loop Supply Chain

Abstract

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.

Keywords:

• Closed loop supply chain
• Diffusion control problem
• Heavy traffic analysis
• Local-time processes

Mathematics Subject Classification:

• Primary 60K25, 60K20, 93E20
• Secondary 60K10, 60K30

ACKNOWLEDGMENTS

Arka Ghosh is supported by the NSF grant DMS-0608634. Ananda Weerasinghe is supported by the ARO grants W911NF0510032 and W911NF0710424. We are grateful for their support.