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.