Transshipment of Inventories Among Retailers: Myopic vs. Farsighted Stability

Posted: 12 May 2006

See all articles by Greys Sosic

Greys Sosic

University of Southern California - Marshall School of Business

Abstract

We consider a model of a decentralized distribution system consisting of n retailers selling an identical product. Each retailer faces a stochastic demand, and must order her initial inventory before this demand is realized. After demand realization, retailers decide how much of their unsold inventory or unsatisfied demand they want to share with the other retailers. This is followed by a transshipment of leftover inventories, and distribution of the additional profit generated through inventory sharing.

In this paper, we address the following issue: Suppose that the retailers distribute the profit from inventory sharing according to an allocation rule that induces retailers to share their residuals in a way that maximizes the additional profit, such as the Shapley value, but may not belong to the core. Is it likely that, in this framework, all retailers will jointly share their residuals and not form subcoalitions? Previous research looked at this problem from a myopic viewpoint, and concluded that the grand coalition is not stable. Unlike the prior work, in this paper we look at stability in a farsighted sense. That is, we assume that retailers consider not only their immediate payoffs, but are also concerned with reactions of other retailers to their actions. We show that in a symmetric setting, with identical additional unit revenues from transshipments generated by all retailers, farsighted retailers always maximize their allocations by not defecting from the grand coalition. We also provide conditions when the same is true for non-identical additional unit revenues.

Keywords: Inventory sharing, coalitions, cooperative games, coalition stability

JEL Classification: C71

Suggested Citation

Sosic, Greys, Transshipment of Inventories Among Retailers: Myopic vs. Farsighted Stability. Management Science, Forthcoming, Marshall School of Business Working Paper No. IOM 05-06, Available at SSRN: https://ssrn.com/abstract=900750

Greys Sosic (Contact Author)

University of Southern California - Marshall School of Business ( email )

Bridge Hall 308
Los Angeles, CA California 90089
United States

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