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 facil ity. The demand for the product is random, and it is independent and identi cally distributed from period to period. The demand is observed at the begi nning of a time period, but it need not be filled until the end of the peri od. Unfilled demand is backordered. A base stock or order-up-to policy is u sed. The shortfall is the order-up-to level minus the inventory position. T he inventory system is easily understood and managed if we know the distrib ution of the shortfall. We develop a new approximation for this distributio n, and perform extensive computational tests of existing approximations. Ou r new approximation works extremely well as long as the coefficient of vari ation of the demand is less than two. Far practical applications this is by far the most interesting case; No known approximations work well consisten tly when the coefficient of variation of the demand is greater than two.