A Finite Horizon Dynamic Inventory Model with a Stockout Constraint

Abstract

A finite horizon, periodic review, dynamic inventory model for a single item with a stockout constraint is considered in this paper, and the optimal ordering policy is obtained. The discrete case is dealt with, and linear purchase and holding costs are assumed together with a fixed order cost, all costs being discounted back to the beginning of the first period. A fixed delivery lead time is assumed, and backlogging of unsatisfied demand is required. The stockout constraint is that the ratio of the expected number of stockouts to the expected demand over the finite horizon not exceed a preassigned fraction. The optimal ordering policy is obtained by the usual dynamic programming technique, using a Lagrange multiplier to handle the stockout constraint.