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Estimating the lead‐time demand distribution for an autocorrelated demand by the pearson system and a normal approximation

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  • Bong‐Geun An
  • Stergios B. Fotopoulos
  • Min‐Chiang Wang

Abstract

The exact first four moments of lead‐time demand L are derived for an AR(1) and a MA(1) demand structures where the arbitrary lead‐time distribution is assumed to be independent of the demand structure. These moments then form a basis for the Pearson curve‐fitting procedure for estimating the distribution of L. A normal approximation to L, a version of the central limit theorem, is obtained under some general conditions. Reorder points (ROPs) of an inventory system are then estimated based on the Pearson system and a normal approximation. Their performances are evaluated. Numerical investigation shows that the Pearson system performs extremely well. The normal approximation, however, is good only for some limited cases, and is sensitive to the choice of the lead‐time distribution. A possible improvement is noted.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:36:y:1989:i:4:p:463-477
    DOI: 10.1002/1520-6750(198908)36:43.0.CO;2-R
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    2. 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.
    3. C. S. Davis & M. A. Stephens, 1983. "Approximate Percentage Points Using Pearson Curves," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 32(3), pages 322-327, November.
    4. Fotopoulos, Stergios & Wang, Min-Chiang & Rao, S. Subba, 1988. "Safety stock determination with correlated demands and arbitrary lead times," European Journal of Operational Research, Elsevier, vol. 35(2), pages 172-181, May.
    5. Chandrasekhar Das, 1976. "Explicit formulas for the order size and reorder point in certain inventory problems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 25-30, March.
    6. Wang, Min-Chiang, 1987. "Estimating the lead-time demand distribution when the daily demand is non-normal and autocorrelated Hon-Shiang LAU," European Journal of Operational Research, Elsevier, vol. 29(1), pages 60-69, April.
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