The (S − 1, S) Inventory Model with Arbitrary Back-Ordered Demand and Constant Delivery Times

This paper derives the important measures of supply performance for an inventory model in which the replenishment policy is to reorder a unit whenever demand occurs. The performance measures considered are: the expected number of back-orders; the expected resupply and stockout times; and the probability distribution for resupply times. All demands, described by an arbitrary distribution, are captured, but need not necessarily be satisfied immediately. The delivery times are assumed constant. Also considered is the problem of trade-offs between spares and the delivery time to achieve a given level of supply performance at least cost.