Optimizing centralized inventory operations in a cooperative game theory setting

Abstract

For single period inventory models with normally distributed, correlated individual demands we examine the problem of minimizing the cost of inventory centralization as a function of the covariance matrix. In a stable centralized setting there are no incentives for any party to break-away -referred to as nonempty core conditions. For the allocated benefits in inventory centralization, nonempty core conditions are always satisfied. In this paper we discuss a step by step greedy optimization procedure which computes an optimal centralization solution. The procedure manipulates the correlations without changing the mean or the variance at each store. We do not just accept that in the centralized setting the parties are better-off, but for the first time provide the analysis of how to maximize their collective benefits.

Game-Theoretic Analysis of Cooperation Among Supply Chain Agents: Review and Extensions

“…Hartman et al (2000) prove the non-emptiness of the core for a single period inventory model with n players facing demands with symmetric distributions, and for players facing joint multivariate normal demand distribution. Hartman and Dror (2003) show the non-emptiness of the core for a single period inventory model with n players facing normally distributed, correlated individual demands. Müller et al (2003) strengthen their results by showing non-emptiness of the core for all possible joint distributions of demand.…”

Cooperative Logistic Games

“…They showed the (restrictive) condition under such a cooperative game has a non-empty core and conjectured that the core is non-empty at least for independent demands. (Hartman & Dror, 2003) proved the non-emptiness of the core for a single period inventory game with n retailers experiences normally distributed, correlated individual demands. On the other hand, (Müller et al, 2002) proved a stronger result than that conjectured by (Hartman et al, 2000).…”

Stable Group Purchasing Organizations

“…The core was introduced to the operations literature in Hartman and Dror (1996) in the newsvendor context and has since then been widely adopted (for example see Hartman et al 2000, Hartman and Dror 2003, 2005, Chen and Zhang 2008. Thus, in order to induce participation of all buyers in the GPO, one may want to select core allocations.…”