Stochastic models for inventory management at service facilities

We consider a facility that provides service to customers using items of inventory. Assuming instantaneous order replenishments, we show that under both the expected discounted cost and the average cost per unit time criteria, the optimal policy is patient, that is, never to order when the system is empty, to place an order only when the inventory level drops to zero, and a threshold ordering policy is optimal. We also model the case where the queueing capacity is finite and the arriving customers who finds that the queue is full are rejected with penalties. Provided that the delay of serving a customer is always less costly than the cost of a rejected customer, we show that the optimal policy has the same properties as the infinite queueing system. We also present a simple heuristic policy for the problem and provide computational results.