Order-based backorders and their implications in multi-item inventory systems

In a multi-item inventory system, such as an assemble-to-order manufacturing system or an online-retailing system, a customer order typically consists of several different items in different amounts. The average order-based backorders are the average number of customer orders that are not yet completely filled. While this is an important measure of customer satisfaction, it has not been widely studied in the operations management literature. This is largely because its evaluation involves the joint distribution of inventory levels of different items and other intricate relations, which is computationally dreadful. Taking a novel approach, this paper develops a tractable way of evaluating this measure exactly. We also develop easy-to-compute bounds, which require the evaluation of item-based backorders only. Numerical experiments indicate that the average of the lower and upper bounds is very effective. The exact results show surprisingly simple structures, which shed light on how system parameters affect the performance. Using these results, we study several examples to gain managerial insights. Questions addressed include: What are the implications of item-based inventory planning decisions on the order-based performance? What is the impact of introducing common components on inventory and service trade-offs? Would order-delivery performance be improved if we restrict the number of choices in product configurations?