This paper studies optimal (s, S) policies for production planning in one-machine manufacturing systems. The machine produces one type of product with delivery time guarantees on the products offered to the customers. The inter-arrival time of the demand and the processing time for one unit of product are assumed to be exponentially distributed. The total delivery time (total lead time) consists of two parts: the cycle time and the delivery time. The cycle time is the time between the arrival of an order and the time requested product leaves the manufacturing system. The delivery time is the time from the manufacturing system to the customer. We model the delivery time by a shifted exponential distribution. Unbiased and consistent estimators are derived for this distribution. The analytical form of the steady state probability distribution for the inventory levels is derived. The average profit of the system can be written in terms of the resulting probability distribution. Hence the optimal (s, S) policy can be obtained by varying different possible values of s and S.
