The (S − 1, S) Inventory Model under Time Limit on Backorders

Abstract

Existing models of inventory control assume that when a stockout occurs customers either wait as long as necessary or not at all for the replenishment to arrive. This paper introduces a more realistic assumption—customers are assumed to wait a fixed amount of time before cancelling their orders. The new assumption is incorporated in the (S − 1, S) inventory model, which is appropriate for slow-moving items. Statistical and economic measures of performance for the model are developed on the basis of certain queuing results. We then use optimization techniques to derive a minimum-cost inventory policy with or without constraints on service levels. We also derive an optimal policy for trade-offs between inventory levels and replenishment rates and provide computational approaches.