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Cost Allocation for Joint Replenishment Models

Authors: Zhang, Jiawei
Keywords: Cooperative Game;Joint Replenishment;Strong Duality
Issue Date: Jul-2007
Publisher: Stern School of Business, New York University
Series/Report no.: OM-2007-03
Abstract: We consider the one-warehouse multiple retailer inventory model with a sub modular 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 non-empty core. The key to our result is a strong duality theorem for the one-warehouse multiple retailer problem under power-of-two policies.
Appears in Collections:IOMS: Operations Management Working Papers

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