On the suboptimality of (S – 1, S) lost sales inventory policies

This paper considers replenishment policies for the continuous review inventory model with Poisson demand, a fixed lead time on replenishment and lost sales during a stockout. There is a time-dependent stockholding cost and a cost per unit of sale lost but there is no (or negligible) cost associated with placing a replenishment order. The standard policy is to specify a maximum stock level, S, and place a replenishment order whenever a demand occurs and is met. This is commonly referred to as an (S – 1, S) policy. It is shown that there are other replenishment policies which give lower-cost solutions. In fact it is demonstrated that an (S – 1, S) policy can never be optimal if S ⩾ 2.