The Evaluation of Order-Based Backorders in Multi-Item Inventory Systems unders,S Policy

Abstract

A multi-item inventory system serves multiple types of customer orders. A customer order may request more than one type of items, with types of items requested varying across the types of customer orders. The inventory of each type of items is managed by a (s, S) policy with constant replenishment order leadtime, where the re-order points, order-up-to quantities, and leadtimes of items can be type dependent. The average order-based backorders (i.e., the average number of orders that wait in system) is an important performance measure for such an inventory system. Because of the dependence in the requests of items, it is generally hard to evaluate the average order-based backorders. Previous studies give sufficient conditions such that the distribution of the joint inventory positions is from independent, uniform distributions. Here we find the necessary and sufficient condition for such a joint distribution. Under the condition, we evaluate the average order-based backorders of each type of orders, and propose bounds and approximations for the performance measure.