Stability and Endogenous Formation of Inventory Transshipment Networks

Abstract

This paper studies a cooperative game of inventory transshipment among multiple rms. In this game, rms rst make their inventory decisions independently, and then decide collectively how to transship excess inventories to satisfy unmet demands. In modeling transshipment, we use networks of rms as the primitive, which o¤er a richer representation of relationships among rms by taking the coalitions used in all previous studies as special cases. For any given cooperative network, we construct a dual price allocation under which the network is stable for any residual demands and supplies in the sense that no rms nd it more pro table to form subnetworks. Under the allocation based on the marginal contribution of each rm to its network (called the MJW value), we show that various network structures such as complete, hub-spoke, and chain networks are stable only under certain conditions on residual amounts. Moreover, these conditions di¤er across network structures, implying that a network structure plays an important role in establishing the stability of a decentralized transshipment system. Finally, we consider the case when rms establish networks endogenously, and show that pairwise Nash stable networks underperform the corresponding networks in centralized systems. Subject classi cations: Games/group decisions: Cooperative. Networks. Inventory. Area of review: Manufacturing, Service, and Supply Chain Operations.