An (s, S) inventory system with Poisson demands and exponential lead time

Abstract

This paper considers a stochastic inventory system with Poisson demand and exponentialy distributed delivery time. Unsatisfied demand is lost. Optimality of an s, S policy and D = S–s ≥ s are assumed. The steady state probabilities of the system are calculated, average costs are obtained and the minimized. Two limiting cases may be solved in closed form: rate of demand much larger or much smaller than rate of delivery. In the last case the Wilson lot size formula is regained. Stochastic inventory systems have been studied extensively in the literature (see, for example, Arrow, Karlin and Scarf 1958. Hadley and Within 1963, Veinott and Wagner 1966, Beckmann 1961, Kaplan 1970, Simon 1971, Sivazlian 1974)