A production model with delivery time guarantees for manufacturing systems with early set-up

We consider optimal (s, S) policies with delivery time guarantees for production planning in manufacturing systems with early set-up. 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. A set-up time is required for the machine. We model the set-up by the exponential 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 this probability distribution. Hence the optimal (s, S) policy can be obtained by varying different possible values of s and S.