Transshipment of Inventories Among Retailers: Myopic vs. Farsighted Stability
Management Science, Forthcoming
Posted: 12 May 2006
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: Suggested Citation