Capacity allocation and inventory policy in a distribution system

We consider a single-period distribution system with one supplier and two retailers. The supplier may have infinite or finite capacity. The demand at each retailer is random. When a stockout occurs at one retailer the customer may go to the other retailer. We study both the decentralized and centralized inventory control problems. For the decentralized problem we show that a unique Nash equilibrium exists when the capacity at the supplier is infinite. However, when the capacity is finite, only under certain conditions does the Nash equilibrium exist. For centralized inventory control we obtain the optimal allocation that maximizes the expected profit of the entire supply chain. For the case of decentralized controls we also design channel coordination mechanisms, i.e., a decentralized cost structure resulting in a Nash equilibrium with chain-wide profits equal to those achieved under a fully centralized system. We compare the performance of two retailers in the decentralized and centralized controls and analyze the impact of channel coordination on the whole supply chain.