On the (s,S) policy with fixed inventory holding and shortage costs

In this paper, the authors consider a dynamic stochastic inventory model with fixed inventory holding and shortage costs in addition to a fixed ordering cost. They discuss a sufficient and necessary condition for an (s,S) policy to be optimal in the class of such stochastic inventory models. Furthermore, the authors explore how such a sufficient and necessary condition can be rewritten when the demand distribution is specified. Several examples such as uniform, exponential, normal and gamma distribution functions are treated. The main purpose of this paper is to show that the (s,S) policy is still optimal under a simple condition even if fixed inventory costs are involved. Although Aneja and Noori consider a similar mode only with fixed inventory shortage cost, the present proof for the optimality of an (s,S) policy in the multi-period model is different from a much simpler than theirs.