Replenish-up-to inventory control policy with stochastic replenishment intervals for perishable merchandise

The multi-cycle inventory problems have been studied under two main assumptions. Continuous review assumption where an order can made at any time depending on inventory position and periodic review assumption where an order can be initiated only at discrete time epochs. In this study, we analyze a multi period inventory problem that falls under neither of these two assumptions. In this case we consider that there are periodic replenishments but the replenishment intervals are taken to be i.i.d. random variables. This setting represents the real life cases where a supplier visits a retailer with random arrival time and the retailer replenishes his inventories based on a replenish-up-to-level inventory control policy. We also assume that only a certain fraction of unmet demand is backordered and the rest of it is lost. At last, we assume the goods is perishable, and has constant deteriorating rate. In this setting under general distribution between replenishment epochs, we give the condition that must hold for the optimal replenish-up-to level.