Inventory Rationing in a Capacitated System with Backorders and Lost Sales

In this paper, we study a periodic review, capacitated, make-to-stock system with two demand classes. The first class demand comes from customers who have long term and profitable relationships with the manufacturer. The second class demand comes from the retail market. The first class demand not satisfied immediately is backordered, whereas the unsatisfied second class demand is lost. There are two fundamental decisions for managing such a system, i.e., production decision and rationing decision. We prove that a base stock rationing policy is optimal. Furthermore, through an extensive numerical study, we study the cost savings of the optimal policy compared with two common used heuristics and show that the benefit of the optimal control policy can be quite significant.