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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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    1. Stephen C. Graves, 1982. "Note---A Multiple-Item Inventory Model with a Job Completion Criterion," Management Science, INFORMS, vol. 28(11), pages 1334-1337, November.
    2. W. Karl Kruse, 1981. "Technical Note—Waiting Time in a Continuous Review ( s , S ) Inventory System with Constant Lead Times," Operations Research, INFORMS, vol. 29(1), pages 202-207, February.
    3. John W. Mamer & Stephen A. Smith, 1982. "Optimizing Field Repair Kits Based on Job Completion Rate," Management Science, INFORMS, vol. 28(11), pages 1328-1333, November.
    4. Shelby Brumelle & Daniel Granot, 1993. "The Repair Kit Problem Revisited," Operations Research, INFORMS, vol. 41(5), pages 994-1006, October.
    5. Ravi Anupindi & Sridhar Tayur, 1998. "Managing Stochastic Multiproduct Systems: Model, Measures, and Analysis," Operations Research, INFORMS, vol. 46(3-supplem), pages 98-111, June.
    6. John W. Mamer & Andrew W. Shogan, 1987. "A Constrained Capital Budgeting Problem with Applications to Repair Kit Selection," Management Science, INFORMS, vol. 33(6), pages 800-806, June.
    7. Hausman, Warren H. & Lee, Hau L. & Zhang, Alex X., 1998. "Joint demand fulfillment probability in a multi-item inventory system with independent order-up-to policies," European Journal of Operational Research, Elsevier, vol. 109(3), pages 646-659, September.
    8. Craig C. Sherbrooke, 1975. "Technical Note—Waiting Time in an ( S − 1, S ) Inventory System—Constant Service Time Case," Operations Research, INFORMS, vol. 23(4), pages 819-820, August.
    9. Kenneth R. Baker & Michael J. Magazine & Henry L. W. Nuttle, 1986. "The Effect of Commonality on Safety Stock in a Simple Inventory Model," Management Science, INFORMS, vol. 32(8), pages 982-988, August.
    10. Yigal Gerchak & Michael J. Magazine & A. Bruce Gamble, 1988. "Component Commonality with Service Level Requirements," Management Science, INFORMS, vol. 34(6), pages 753-760, June.
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