The (S-1, S) Inventory Model with Order Size Dependent Delivery Times

Abstract

This paper considers (S-1, S) inventory models which have wide applications in reparable spare parts inventory systems and multi-echelon systems. We assume a discrete compound Poisson demand and order size dependent delivery times: when the replenishment order size is n, we assume the delivery time distribution is arbitrary with finite mean b. On the basis of the fact the outstanding orders follow a certain queueing process, we introduce the results of Fakinos (1982). We develop the efficient recursive formulae to find the optimal S under several performance measures as a function of the decision variable S. The results of this paper can be applied to the multi-echelon systems such as METRIC.