Admission control for a capacitated supply system with real-time replenishment information

Abstract

Control towers can provide real-time information on logistic processes to support decision making. The question however, is how to make use of it and how much it may save. We consider this issue for a company supplying expensive spare parts and which has limited production capacity. Besides deciding on base stock levels, it can accept or reject customers. The real-time status information is captured by a k-Erlang distributed replenishment lead time. First we model the problem with patient customers as an infinite-horizon Markov decision process and minimize the total expected discounted cost. We prove that the optimal policy can be characterized using two thresholds: a base work storage level that determines when ordering takes place and an acceptance work storage level that determines when demand of customers should be accepted. In a numerical study, we show that using real-time status information on the replenishment item and adopting admission control can lead to significant cost savings. The cost savings are highest when the optimal admission threshold is a work storage level with a replenishment item halfway in process. This finding is different from the literature, where it is stated that the cost increase of ignoring real-time information is negligible under either the lost sales or the backordering case. Next we study the problem where customers are of limited patience. We find that the optimal admission policy is not always of threshold type. This is different from the literature which assumes an exponential production lead time.