A Stochastic Programming Duality Approach to Inventory Centralization Games

Abstract

In this paper, we present a unified approach to study a class of cooperative games arising from inventory centralization. The optimization problems corresponding to the inventory games are formulated as stochastic programs. We observe that the strong duality of stochastic linear programming not only directly leads to a series of recent results concerning the non-emptiness of the cores of such games, but also suggests a way to find an element in the core. The proposed approach is also applied to inventory games with concave ordering cost. In particular, we show that the newsvendor game with concave ordering cost has a non-empty core. Finally, we prove that it is NP-hard to determine whether a given allocation is in the core for the inventory games even in a very simple setting.