Customer Waiting Times in Continuous Review (nQ,R) Inventory Systems with Compound Poisson Demand

The probability distribution of customer waiting times due to stock-outs and backlogging is studied, including mean and variance, when demand follows a compound Poisson process and the inventory is governed by an (nQ,R) inventory policy under continuous review. Existing results are reviewed and new exact contributions are presented, particularly covering the case when R<–1, a case that quite often may be optimal for central warehouses, but is missing in the literature. Waiting times are investigated for two cases: For an average unit of demand, assuming partial deliveries, and for a customer demandingd units, assuming full deliveries only. Here d may be interpreted as the constant order size from a specific customer/retailer. The results are easily generalized to the waiting time of an average customer. Besides exact formulae, various approximations and simple heuristics are suggested for calculation of means and variances. The results should be valuable for approximately optimal inventory control in distribution