A production/inventory system is considered in which a production facility produces one type of product. The demand for the product is given by a compound Poison process and is supplied directly from inventory when inventory is available and is lost when inventory is out of stock. The processing time to produce one item is assumes to follow a general distribution. An (s, S) policy is considered in which production stops at the instant the stock on hand reachs S and the setup of the production facility begins at an inspection point when the stock on hand drops to or below s for the first time. The time interval between two successive inspection points during a non-production period is a random variable which follows a general distribution.