The (r, q) inventory policy, in which the replenishment quantity q is ordered, when the inventory position reaches the reorder point r, is one of the most widely practiced control policies for single-stage, single-item inventory systems. This policy has been thoroughly studied under the scenario, in which demand is backordered, whenever it cannot be satisfied immediately from inventory. More sparsely studied is the case where unfilled demand is either lost or satisfied from outside the considered system. One reason is that fundamental results from the backorder case do not hold in the case of lost sales, which makes the latter much more complicated to model exactly, particularly when several replenishment orders might be outstanding simultaneously. Nevertheless, the lost-sales case has considerable practical significance. Especially, in sectors like retails and spare parts it is frequently observed as the standard business practice in case of shortages. Moreover, analyses of this setting can assist in better understanding of more complex settings, such as when (r, q) inventory control systems are employed as building blocks of supply chain structures in which lost sales play a significant role. In this paper, we consider a single-item inventory system with lost sales controlled by a continuous review (r, q) policy. Demand is Poisson and lead times are assumed to be constant. For a standard cost structure our focus is on analyzing the long-run average cost and fill-rate performance measures. In order to specify these performance measures, we apply simple approximations. We evaluate the approximations by making comparisons to results obtained using exact, but also more elaborate analytical models, as well as simulation experiments. An appropriate choice of approximation may simplify performance evaluation and be of use in guiding policy decisions of the inventory control system under consideration. Further research involves extending the analyses to include the case when lead times are stochastic.
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International Conference on Flexible Supply Chains in a Global Economy, 2008