An Inventory Allocation System with Backorders and Sales Rejection

We consider a variant of the periodic review system with a virtual warehouse that is due to Eppen and Schrage (1981). Depending on the realized pattern of demand during the delivery leadtime, this inventory is dynamically allocated or rationed to each of the retailers. While Eppen and Schrage (1981) assume that all unfilled demand is backordered, we allow some demand to be rejected to keep inventories in balance. This results in an exact analysis of the system. We develop conditions for the unique solution in a two retailer model and discuss the implications for the multi-retailer systems. Our analysis works for both discrete and continuous demands. Illustrative numerical examples suggest that, with our policy, only a very small fraction of demand would be rejected. The scope of our policy for general distribution and transshipment models has been explained.