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Expressions for item fill rates in periodic inventory systems

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  • M. Eric Johnson
  • Hau L. Lee
  • Tom Davis
  • Robert Hall

Abstract

We examine the problem of estimating the item fill rate in a periodic inventory system. We show that the traditional expressions for line item fill rate, found in many operations management textbooks, perform well for high fill rates (above 90%), but they consistently underestimate the true fill rate. The problem of underestimation becomes significant as the fill rate falls below 90% and is greatly amplified in cases with very low fill rates (below 50%). We review other more accurate expressions for fill rate, discussing their relative merits. We then develop an exact fill rate expression that is robust for both high and low fill rates. We compare the new expression to others found in the literature via an extensive set of simulation experiments using data that reflect actual inventory systems found at Hewlett‐Packard. We also examine the robustness of the expressions to violations in the underlying assumptions. Finally, we develop an alternative fill rate expression that is robust for cases of high demand variability where product returns are allowed. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • M. Eric Johnson & Hau L. Lee & Tom Davis & Robert Hall, 1995. "Expressions for item fill rates in periodic inventory systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(1), pages 57-80, February.
  • Handle: RePEc:wly:navres:v:42:y:1995:i:1:p:57-80
    DOI: 10.1002/1520-6750(199502)42:13.0.CO;2-2
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    References listed on IDEAS

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    1. Arnoud De Meyer & Jinichiro Nakane & Jeffrey G. Miller & Kasra Ferdows, 1989. "Flexibility: The next competitive battle the manufacturing futures survey," Strategic Management Journal, Wiley Blackwell, vol. 10(2), pages 135-144, March.
    2. Hau L. Lee & Corey Billington & Brent Carter, 1993. "Hewlett-Packard Gains Control of Inventory and Service through Design for Localization," Interfaces, INFORMS, vol. 23(4), pages 1-11, August.
    3. Eliezer Naddor, 1978. "Note--Sensitivity to Distributions in Inventory Systems," Management Science, INFORMS, vol. 24(16), pages 1769-1772, December.
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    1. Frank Chen & Jennifer K. Ryan & David Simchi‐Levi, 2000. "The impact of exponential smoothing forecasts on the bullwhip effect," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(4), pages 269-286, June.
    2. Douniel Lamghari-Idrissi & Roy van Hugten & Geert-Jan van Houtum & Rob Basten, 2022. "Increasing Chip Availability Through a New After-Sales Service Supply Concept at ASML," Interfaces, INFORMS, vol. 52(5), pages 460-470, September.
    3. Qi, Mingyao & Yang, Ying & Cheng, Chun, 2023. "Location and inventory pre-positioning problem under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 177(C).
    4. Wang, Xin & Kuo, Yong-Hong & Shen, Houcai & Zhang, Lianmin, 2021. "Target-oriented robust location–transportation problem with service-level measure," Transportation Research Part B: Methodological, Elsevier, vol. 153(C), pages 1-20.
    5. John E. Tyworth & Liam O'Neill, 1997. "Robustness of the normal approximation of lead‐time demand in a distribution setting," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(2), pages 165-186, March.
    6. Saldanha, John P., 2022. "Estimating the reorder point for a fill-rate target under a continuous review policy in the presence of non-standard lead-time demand distributions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 164(C).
    7. Alex X. Zhang, 1997. "Demand Fulfillment Rates In An Assembleto‐ Order System With Multiple Products And Dependent Demands," Production and Operations Management, Production and Operations Management Society, vol. 6(3), pages 309-324, September.

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