Optimal (s, S) policies with delivery time guarantees for manufacturing systems with early set-up

We consider optimal (s, S) policies with delivery time guarantees for produ ction planning in one-machine manufacturing systems with early set-up. The machine produces one type of product and delivery time guarantee is offered to the customers for each unit of ordered product. The inter-arrival time of the demand and the processing time for one unit of product are assumed t o be exponentially distributed. In a (s, S) policy, the machine will shut d own when an inventory level of S is attained and once the inventory level d rops to s, the machine will re-start, A set-up time is required for the mac hine. We model the set-up by the exponential distribution. We obtained an a nalytical form of the steady state probability distribution for the invento ry levels derived. The average profit of the system can be written in terms of this probability distribution. Hence the optimal (s, S) policy can be o btained by varying different possible values of s and S. (C) 2001 Elsevier Science Ltd. All rights reserved.