A NonCooperative Approach to Cost Allocation in Joint Replenishment

Simai He (), Jay Sethuraman (), Xuan Wang () and Jiawei Zhang ()
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Simai He: School of Information Management and Engineering, Shanghai University of Finance and Economics, Shanghai, China 200433
Jay Sethuraman: Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Xuan Wang: Department of Information Systems, Business Statistics and Operations Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Jiawei Zhang: Leonard N. Stern School of Business, New York University, New York, New York 10012; and New York University Shanghai, Shanghai, China 200122

Operations Research, 2017, vol. 65, issue 6, 1562-1573

Abstract: We consider the infinite-horizon multiple retailer joint replenishment problem with first-order interaction. In this model, the joint setup cost incurred by a group of retailers placing an order simultaneously consists of a group-independent major setup cost and retailer-specific minor setup costs. The goal is to determine an inventory replenishment policy that minimizes the long-run average system-wide cost. In this paper, we adopt a noncooperative approach to study the joint replenishment game. We consider the allocation rule in which the major setup cost is split equally among the retailers who place an order together, and each retailer pays his own holding and minor setup costs. Given the preannounced allocation rule, each retailer determines his replenishment policy to minimize his own cost anticipating the other retailers’ strategy. We show that a payoff dominant Nash equilibrium exists, and quantify the efficiency loss of the noncooperative outcome relative to the social optimum. Although the worst-case ratio between the best decentralized outcome and the social optimum is O ((ln n ) 1/2 ), where n is the number of retailers, numerical results suggest that the best equilibrium is near optimal.

Keywords: joint replenishment; cost-sharing game; payoff dominant Nash equilibrium; price of anarchy; price of stability (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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