(s, S) Policies Under Continuous Review and Discrete Compound Poisson Demand

We consider inventory policies for a continuous review system with discrete compound Poisson demand, convex holding-penalty cost and fixed order cost. Beckmann has showri that under these conditions (s, S) policies are optimal. We develop recursive formulae to calculate the cost for any pair (s, S). Relations among s, S, S − s and the cost are produced that lead to an efficient determination of the optimal s and S. Tighter bounds are utilized than those obtained by Veinott and Wagner for the analogous case of periodic review. Sensitivity considerations are discussed.