A centralized ordering and allocation system with backorders and strategic lost sales

This article considers a multi-retailer distribution system that is managed by a central decision maker who, at the start of each period, determines how much to order to replenish the system stock. The decision maker also determines how to allocate incoming pipeline inventory to maintain inventory balance among the retailers. It has been noted in the literature that balancing inventories can equalize service levels among retailers. To improve the efficacy of the allocation, this article allows some demand to be rejected to keep inventories in balance. Consequently, depending on the realized pattern of demand during the delivery lead time, the inventory is dynamically allocated to each of the retailers. For the model with two retailers, an exact representation of the infinite-horizon long-run average cost function is developed. This exact expression is used to develop conditions for the unique solution for the two-retailer case. The presented analysis holds for a wide class of continuously and discretely distributed demand.