A Non-Cooperative Approach to Cost Allocation in Joint Replenishment

48 Pages Posted: 29 Sep 2014 Last revised: 31 Aug 2017

See all articles by Simai He

Simai He

Shanghai University of Finance and Economics

Jay Sethuraman

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Xuan Wang

Hong Kong University of Science and Technology, ISOM Department

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences

Date Written: September 27, 2014

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 non-cooperative 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 (N.E.) exists, and quantify the efficiency loss of the non-cooperative outcome relative to the social optimum. Although the worst-case ratio between the best decentralized outcome and the social optimum is O (sqrt{ln n}), 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

Suggested Citation

He, Simai and Sethuraman, Jay and Wang, Xuan and Zhang, Jiawei, A Non-Cooperative Approach to Cost Allocation in Joint Replenishment (September 27, 2014). Available at SSRN: https://ssrn.com/abstract=2502409 or http://dx.doi.org/10.2139/ssrn.2502409

Simai He

Shanghai University of Finance and Economics ( email )

777 Guoding Road
Shanghai, AK Shanghai 200433
China

Jay Sethuraman

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Xuan Wang (Contact Author)

Hong Kong University of Science and Technology, ISOM Department ( email )

Clear Water Bay
Kowloon
Hong Kong, Not Applicable
Hong Kong
852-23585854 (Phone)

Jiawei Zhang

New York University (NYU) - Department of Information, Operations, and Management Sciences ( email )

44 West Fourth Street
New York, NY 10012
United States

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