Discounted Cost Models with Backorders

One of the most important developments in the inventory theory has been to show that (s, S) policies are optimal for a class of dynamic inventory models with random periodic demands and fixed ordering costs. Under an (s, S) policy, if the inventory level at the beginning of a period is less than the reorder point s, then a sufficient quantity must be ordered to achieve an inventory level S, the order-up-to level, upon replenishment. There are a number of papers in the literature devoted to proving the optimality of (s, S) policies under a variety of assumptions. However, in real-life inventory problems, some of these assumptions do not hold. It is our purpose to relax these assumptions toward realism and still demonstrate the optimality of (s, S)-type policies.