We consider a continuous review (s, S) model of perishable items with lost sales. Once items are perished the entire inventory drops instantaneously to zero. The total cost includes the cost of: ordering, unsatisfied demand, units destroyed, holding, and fixed cost of perishability. Both the time to perishability and the lead times are assumed to be exponentially distributed while two cases of demand distribution are considered: Poisson and compound Poisson with general demand sizes. We study the average cost criterion and provide computational results on the problem of finding the optimal re-order level, s, and order up-to level, S. None of the known work on the subject is as general as the model presented here. Our analysis leads to several insights on the optimal (s, S) policies for perishable items in the presence of lead times. For example, we demonstrate that the effectiveness of a heuristic that ignores perishability (and is also analyzed here) decreases with the demand variability and that the cost may either increase or decrease with this variability.
