A General Decomposition Algorithm for Parallel Queues with Correlated Arrivals
Queueing Systems: Theory and Applications
Optimal Control of a High-Volume Assemble-to-Order System
Mathematics of Operations Research
Queueing Systems: Theory and Applications
Managing an Assemble-to-Order System with Returns
Manufacturing & Service Operations Management
The Value of Component Commonality in a Dynamic Inventory System with Lead Times
Manufacturing & Service Operations Management
No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems
Operations Research
Mathematics of Operations Research
Consideration of purchase dependence in inventory management
Computers and Industrial Engineering
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A customer order to a multi-item inventory system typically consists of several different items in different amounts. The probability of satisfying an arbitrary demand within a prespecified time window, termed the order fill rate, is an important measure of customer satisfaction in industry. This measure, however, has received little attention in the inventory literature, partly because its evaluation is considered a hard problem. In this paper, we study this performance measure for a base-stock system in which the demand process forms a multivariate compound Poisson process and the replenishment leadtimes are constant. We show that the order fill rate can be computed through a series of convolutions of one-dimensional compound Poisson distributions and the batch-size distributions. This procedure makes the exact calculation faster and much more tractable. We also develop simpler bounds to estimate the order fill rate. These bounds require only partial order-based information or merely the item-based information. Finally, we investigate the impact of the standard independent demand assumption when the demand is actually correlated across items.