TITLE: The Joint Replenishment Problem Revisited: A Cost Allocation Perspective

SPEAKER: Jiawei Zhang, Assistant Professor of Operations Management
The Stern School of Business, New York University

DATE / TIME: Friday, April 25, 2008 / 2:30 - 3:45 p.m.

LOCATION: Room 453 Mohler Lab, 200 W. Packer Avenue

ABSTRACT: We consider the classical joint replenishment problem with a submodular joint setup cost function. The objective of this model is to determine an inventory replenishment policy that minimizes the long-run average system cost over an infinite time horizon. Although the optimal policy for this problem is still unknown, a class of easy-to-implement power-of-two policies are 98% effective. In this talk, we assume that the inventory system consists of retailers that belong to different firms or are decentralized divisions of the same firm. We discuss how the system-wide cost, under an optimal power-of-two policy, should be allocated to the retailers. This question generates an interesting cooperative game. We prove that this cooperative game is submodular. We propose a simple and intuitive core allocation for this game. We also show that this core allocation leads to a population monotonic allocation scheme. All these results are derived using a strong duality property of the joint replenishment problem.

BIOGRAPHY: Jiawei Zhang is an Assistant Professor of Operations Management at the Stern School of Business, New York University. He received a B.S. degree in Applied Mathematics and an M.S. degree in Operations Research from Tsinghua University, and a Ph.D. in Operations Research from Stanford University. His research interests include Cost Allocation in Supply Chain Management, Deterministic and Stochastic Optimization, and Approximation Algorithms. He has published in journals that include Mathematical Programming, Mathematics of Operations Research, Operations Research, Psychometrika, SIAM Journal on Computing, etc. He was a recipient of the INFORMS Optimization Prize for Young Researchers in 2004.