Continuous Review (s, S) Policies with Lost Sales

A method is developed to calculate an (s, S) policy that minimizes the average stationary cost in an inventory system with: constant lead time, fixed order cost, linear holding cost per unit time, linear penalty cost per unit short, discrete compound Poisson demand, and lost sales. It is assumed that at most one order is outstanding, or equivalently that S − s > s. The procedure is compared to several easier-to-compute approximate solutions, including one that assumes backordering. Examples are given that reveal that although the backorder solution is different than the lost sales one, the cost penalty of using it in the lost sales situation is small.