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Modeling lead‐time demand for lumpy demand and variable lead time

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  • Uttarayan Bagchi

Abstract

Slow‐moving items that occasionally exhibit large demand transactions are known as lumpy demand items. In modeling lumpy demand patterns, it is often assumed that the arrival of customer orders follows a Poisson process and that the order sizes are given by the geometric distribution. This gives rise to a stuttering Poisson (sP) model of lumpy demand. If lead times are constant, the result is a stuttering Poisson model of lead‐time demand. Heretofore, authors such as Ward [18] and Mitchell, Rappold, and Faulkner [12] have assumed constant lead times and thus stopped at the sP model. We develop this model further by introducing the effect of lead‐time variability. For illustration, we use the normal and the gamma distributions as characterizations of lead time. The resulting models of lead‐time demand are referred to as the geometric Poisson normal (GPN) and the geometric Poisson gamma (GPG). For both these models, the article derives tractable expressions for calculating probabilities. Errors introduced by using the sP, constant lead‐time model instead of the exact, variable lead‐time model are also illustrated.

Suggested Citation

  • Uttarayan Bagchi, 1987. "Modeling lead‐time demand for lumpy demand and variable lead time," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(5), pages 687-704, October.
    • Handle: RePEc:wly:navres:v:34:y:1987:i:5:p:687-704
    DOI: 10.1002/1520-6750(198710)34:53.0.CO;2-B
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    References listed on IDEAS

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    1. C. R. Mitchell & R. A. Rappold & W. B. Faulkner, 1983. "An Analysis of Air Force EOQ Data with an Application to Reorder Point Calculation," Management Science, INFORMS, vol. 29(4), pages 440-446, April.
    2. Steven Nahmias & W. Steven Demmy, 1982. "The logarithmic poisson gamma distribution: A model for leadtime demand," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 29(4), pages 667-677, December.
    3. Craig C. Sherbrooke, 1968. "Discrete compound poisson processes and tables of the geometric poisson distribution," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 15(2), pages 189-203, June.
    4. Donald L. Bott, 1977. "Compound distributions with efficient computation in inventory model applications," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 24(3), pages 407-416, September.
    5. J. B. Ward, 1978. "Determining Reorder Points When Demand is Lumpy," Management Science, INFORMS, vol. 24(6), pages 623-632, February.
    6. Harvey M. Wagner, 1980. "Feature Article—Research Portfolio for Inventory Management and Production Planning Systems," Operations Research, INFORMS, vol. 28(3-part-i), pages 445-475, June.
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    Cited by:

    1. Mahdavi, Mojtaba & Olsen, Tava Lennon, 2021. "The dual-serving problem: What is the right choice of inventory strategy?," Omega, Elsevier, vol. 103(C).
    2. Bong‐Geun An & Stergios B. Fotopoulos & Min‐Chiang Wang, 1989. "Estimating the lead‐time demand distribution for an autocorrelated demand by the pearson system and a normal approximation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 36(4), pages 463-477, August.

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