Rationing game with transshipment in a supply chain of two retailers

Abstract

We consider a two-retailer supply chain where retailers are supplied by a single supplier with uncertain capacity and allowed to implement transshipment between them. When the supplier allocates her scarce capacity in proportion to orders, the retailers compete for her capacity by inflating their orders, i.e., they play the rationing game. The retailers also cooperate with each other by transshipping surplus stock to another who is stocked out. After examining the existence and uniqueness of a Nash equilibrium in order quantities, we analyze how retailers manipulate their orders in the rationing game when transshipment is allowed. Interestingly, we find that, in the rationing game, retailers with transshipment do not necessarily inflate their orders and can strategically order less than their desired amounts. We also characterize the centralized order decisions and make a comparison between the centralized and decentralized orders (i.e., equilibrium orders). Finally, we examine the existence of a pair of transshipment prices that induces the retailers to make the centralized order decisions. We show that such a pair of coordinating prices is harder to exist in the rationing game than in the case of infinite capacity.harder to exist in the rationing game than in the case of infinite capacity.