Inventory management of multi-item systems with order size constraint

Manufacturing and transportation costs have increased substantially in recent years as demands for raw materials and fossil-based energy continue to grow. To buffer potential loss and increase order quantity, manufacturers often specify requirements when retailers place orders. One widely applied practice is to set up a minimum order size requirement, which is largely driven to achieve improved economies in the production and transportation processes. Many buyers, on the other hand, are left perplexed as to how to effectively establish their inventory policies. In this article, we study a multi-item model in which a retailer faces a minimum order size requirement from its manufacturer and the demands for these items are stochastic. In particular, the total order size of all items has to be at least the minimum order size whenever the retailer decides to place an order. We construct the exact model and develop an accurate lower bound approximation. To better understand the dynamics of the system and the ordering behaviour, we characterise important properties and based on which we propose effective heuristic strategies of simple structure for the multi-item model. Through extensive numerical studies, we show that the policies are consistently robust under a variety of different parameters. Important insights into the systems are also provided. © 2010 Taylor & Francis