This paper is concerned with the synthesis of control policies for inventory systems in which the items experience lumpy demands. The nature of the customer demands is approximated by a discrete stuttering Poisson distribution and a continuous review (s,S) inventory policy is used to control such items. A cutoff point is also incorporated into the control policy such that customer orders with transaction sizes greater than the cutoff point will be filtered out of the inventory system and satisfied by placing a special replenishment order to a higher echelon. Customer orders with transaction sizes less than or equal to the cutoff point will be met from stock. It is also specified that if the available inventory is below the order-up-to level S at the time when a special replenishment order is placed, such a replenishment order will also raise the available inventory level to S. A search procedure is presented for determining the optimal values of the control parameters w, s and S. A numerical example is used to illustrate the theoretical results obtained.
