Order arrival control of an M/M/1 failure prone service station

Just-in-time (JIT) manufacturing calls for timely deliveries of the raw materials from the suppliers. Suppliers that cannot deliver by the due dates often face huge penalties. Via careful administration of the order acceptance process, a supplier can adjust the work load of its system and avoid the high penalties due to late deliveries. This paper models the supplier as an M/M/1 service station which is susceptible to failure and studies the optimal arrival control policy for such a system. We prove that the optimal policy is of control limit type and the optimal control rejects more arriving orders when the service station is down.