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On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System

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  • Jing-Sheng Song

    (University of California at Irvine, Irvine, California)

Abstract

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.

Suggested Citation

  • Jing-Sheng Song, 1998. "On the Order Fill Rate in a Multi-Item, Base-Stock Inventory System," Operations Research, INFORMS, vol. 46(6), pages 831-845, December.
    • Handle: RePEc:inm:oropre:v:46:y:1998:i:6:p:831-845
    DOI: 10.1287/opre.46.6.831
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    References listed on IDEAS

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