A real-time decision rule for an inventory system with committed service time and emergency orders

In this paper, we study the inventory system of an online retailer with compound Poisson demand. The retailer normally replenishes its inventory according to a continuous review (nQ, R) policy with a constant lead time. Usually demands that cannot be satisfied immediately are backordered. We also assume that the customers will accept a reasonable waiting time after they have placed their orders because of the purchasing convenience of the online system. This means that a sufficiently short waiting time incurs no shortage costs. We call this allowed waiting time "committed service time". After this committed service time, if the retailer is still in shortage, the customer demand must either be satisfied with an emergency supply that takes no time (which is financially equivalent to a lost sale) or continue to be backordered with a time-dependent backorder cost. The committed service time gives an online retailer a buffer period to handle excess demands. Based on real-time information concerning the outstanding orders of an online retailer and the waiting times of its customers, we provide a decision rule for emergency orders that minimizes the expected costs under the assumption that no further emergency orders will occur. This decision rule is then used repeatedly as a heuristic. Numerical examples are presented to illustrate the model, together with a discussion of the conditions under which the real-time decision rule provides considerable cost savings compared to traditional systems.