Coordinated replenishments with alternative supply sources in two-level supply chains

We consider a two-level supply chain with two warehouses and two retailers. Each facility uses a continuous review (R, Q)-ordering policies for stock replenishments. The retailers are identical and face independent Poisson demands. Each warehouse places orders for replenishments with an outside supplier which has unlimited stocks. Transportation times are constant and all stockouts at both levels are completely backordered. Under normal circumstances, all orders of each retailer are delivered by only one warehouse, which is designated to serve that retailer. But in case that the warehouse is out of stock, there are two alternatives to the retailer: to wait an extra time until the warehouse replenishes its stock or to place an order with the other warehouse. However, the latter decision incurs a higher transportation cost. In this paper, we study two inventory models with alternative supply possibilities and different levels of coordination between warehouses and retailers, and compare the performance of these models with that of a traditional model where ordering from only one of the warehouses is allowed for each retailer.