Order crossover in inventory systems

Order crossovers are usually ignored in iid lead–time inventory systems by using a facilitating assumption, which leads to a one-cycle analysis and an upper bound on the true cost. But the calculation of the probabilities of order crossover can shed light on the magnitude of the departure from the true cost. Here, we first introduce the crossover issue within the context of total cost in the one-vendor continuous review, reorder point, constant demand model so that the need for the calculation of these probabilities is made evident. Second, we present closed-form expressions for the probabilities in one- and two-vendor models. And third, we verify by simulation that our analytical approximation of the true cost is indeed tight