A dynamic inventory model with random replenishment quantities

A periodic-review, random-demand inventory model is analyzed under the assumption that replenishment quantities are random fractions of the amounts ordered. Results of a previous study of a single-period model are generalized to form an easily computed heuristic adaptation of the (s, S) policy for use in this environment. The heuristic is based on the simple practice of scaling down pipeline inventories to estimate the inventory position, and scaling up the order quantity in anticipation of an average replenishment yield. Simulation experiments are used to estimate the most cost-efficient (s, S) policies and to estimate the performance of heuristic policies in environments where replenishment randomness ranges from mild (0-20% defectives) to moderate (0-50% defectives). The heuristic is shown to perform quite well, with expected total costs typically within a few percent of the best (s, S) costs. The results tend to support common practice in industry which is similar to the approach studied here. Although the heuristic is naive in the sense that it ignores the degree of randomness in the replenishment quantity, the simulation results support the speculation that unless the target service level is extremely high, the replenishment process must be extremely random for its variability to be a significant explicit factor in the selection of a practical, cost-effective policy.