Heuristic computation of periodic-review base stock inventory policies

We study the problem of determining production quantities in each period of an infinite horizon for a single item produced in a capacity-limited facility. The demand for the product is random, and it is independent and identically distributed from period to period. The demand is observed at the beginning of a time period, but it need not be filled until the end of the period. Unfilled demand is backordered. A base stock or order-up-to policy is used. The shortfall is the order-up-to level minus the inventory position. The inventory system is easily understood and managed if we know the distribution of the shortfall. We develop a new approximation for this distribution, and perform extensive computational tests of existing approximations. Our new approximation works extremely well as long as the coefficient of variation of the demand is less than two. For practical applications this is by far the most interesting case. No known approximations work well consistently when the coefficient of variation of the demand is greater than two.