Transshipment games with identical newsvendors and cooperation costs

Abstract

In a transshipment game, supply chain agents cooperate to transship surplus products. Although the game has been well studied in the OR literature, the fundamental question whether the agents can afford cooperation costs to set up and maintain the game in the first place has not been addressed thus far. This paper addresses this question for the cooperative transshipment games with identical agents having normally distributed independent demands. We provide characterization of equal allocations which are in the core of symmetric games, and prove that not all transshipment games are convex. In particular, we prove that though individual allocations grow with the coalition size, the growth diminishes according to two rules of diminishing individual allocations. These results are the basis for studying the games with cooperation costs. We model the cooperation costs by the cooperation network topology and the cooperation cost per network link. We consider two network topologies, the clique and the hub, and prove bounds for the cost per link that render coalitions stable. These bounds always limit coalition size for cliques. However, the opposite is shown for hubs, namely newsvendors can afford cooperation costs only if their coalition is sufficiently large.