Inventory and transshipment decisions in the rationing game under capacity uncertainty

In this paper, we consider the inventory decisions of two retailers who are supplied by a single supplier with uncertain capacity. When capacity is allocated in proportion to the retailers? orders, the retailers compete for the capacity by inflating their orders (i.e., the rationing game). In addition, we allow the retailers to implement transshipment between them such that they cooperate by transshipping the surplus stock of one to another who is out of stock. Our analysis of Nash equilibrium orders shows that, while order inflation in the equilibrium orders persists in the rationing game with transshipment, it may not occur if the amount of capacity shortage is small and the transshipment prices are low. Thus, carefully chosen transshipment prices may alleviate order inflation behavior. We also characterize centralized orders that maximize the total profit of the retailers and compare them to equilibrium orders. In particular, we investigate coordinating transshipment prices that induce the retailers to choose centralized orders. Our numerical analysis shows that, even for two identical retailers, coordinating transshipment prices exist in a more limited range of parameter values in the rationing game than they do outside the rationing game due to capacity uncertainty and limitation.