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A comparison of several approximations to the lead time demand distribution

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  • Tadikamalla, Pandu R

Abstract

Several distributions have been used for approximating the lead time demand distribution in inventory systems. We compare five distributions, the normal, the logistic, the lognormal, the gamma and the Weibull for obtaining the expected number of back orders, the reorder levels to have a given protection and the optimal order quantity, reorder levels in continuous review models of (Q, r) type. The normal and the logistic distributions are inadequate to represent the situations where the coefficient of variation (the ratio of the standard deviation to the mean) of the lead time demand distribution is large. The lognormal, the gamma and the Weibull distributions are versatile and adequate; however the lognormal seems to be a viable candidate because of its computational simplicity.

Suggested Citation

  • Tadikamalla, Pandu R, 1984. "A comparison of several approximations to the lead time demand distribution," Omega, Elsevier, vol. 12(6), pages 575-581.
    • Handle: RePEc:eee:jomega:v:12:y:1984:i:6:p:575-581
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    Cited by:

    1. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2023. "A theoretical validation of the DDMRP reorder policy," Computational Management Science, Springer, vol. 20(1), pages 1-28, December.
    2. Anne E. Lordahl & James H. Bookbinder, 1994. "Order‐statistic calculation, costs, and service in an (s, Q) inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(1), pages 81-97, February.
    3. Daniela Favaretto & Alessandro Marin & Marco Tolotti, 2021. "A data-driven and risk-based prudential approach to validate the DDMRP planning and control system," Working Papers 09, Department of Management, Università Ca' Foscari Venezia.
    4. A K Mishra & P R Tadikamalla, 2006. "Order splitting in single sourcing with scheduled-release orders," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(2), pages 177-189, February.
    5. van der Duyn Schouten, F.A. & van Eijs, M.J.G. & Heuts, R.M.J., 1992. "The value of information in a fixed order quantity inventory system," Research Memorandum FEW 568, Tilburg University, School of Economics and Management.
    6. Vernimmen, Bert & Dullaert, Wout & Willemé, Peter & Witlox, Frank, 2008. "Using the inventory-theoretic framework to determine cost-minimizing supply strategies in a stochastic setting," International Journal of Production Economics, Elsevier, vol. 115(1), pages 248-259, September.
    7. Rossetti, Manuel D. & Yasin Ünlü, 2011. "Evaluating the robustness of lead time demand models," International Journal of Production Economics, Elsevier, vol. 134(1), pages 159-176, November.
    8. Hon‐Shiang Lau & Amy Hing‐Ling Lau, 2003. "Nonrobustness of the normal approximation of lead‐time demand in a (Q, R) system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(2), pages 149-166, March.
    9. Halkos, George & Kevork, Ilias & Tziourtzioumis, Chris, 2014. "On the convexity of the cost function for the (Q,R) inventory model," MPRA Paper 55675, University Library of Munich, Germany.
    10. Martí, Joana M. Comas & Tancrez, Jean-Sébastien & Seifert, Ralf W., 2015. "Carbon footprint and responsiveness trade-offs in supply chain network design," International Journal of Production Economics, Elsevier, vol. 166(C), pages 129-142.
    11. 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.
    12. John P. Saldanha & Bradley S. Price & Douglas J. Thomas, 2023. "A nonparametric approach for setting safety stock levels," Production and Operations Management, Production and Operations Management Society, vol. 32(4), pages 1150-1168, April.
    13. van der Duyn Schouten, F.A. & van Eijs, M.J.G. & Heuts, R.M.J., 1992. "The value of information in a fixed order quantity inventory system," Other publications TiSEM ded27036-a7f0-47c7-b799-c, Tilburg University, School of Economics and Management.
    14. Mekhtiev, Mirza Arif, 2013. "Analytical evaluation of lead-time demand in polytree supply chains with uncertain demand, lead-time and inter-demand time," International Journal of Production Economics, Elsevier, vol. 145(1), pages 304-317.

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