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Cost Allocation for Joint Replenishment Models

Department of Information, Operations, and Management Sciences, Stern School of Business, New York University, New York, New York 10012
jzhang{at}stern.nyu.edu

We consider the one-warehouse multiple retailer inventory model 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. This paper focuses on how the 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 has a nonempty core. The key to our result is a strong duality theorem for the one-warehouse multiple retailer problem under power-of-two policies.

Subject classifications: cooperative game; joint replenishment; strong duality.
History: Received December 2006; revision received August 2007; accepted August 2007.