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Non-negative demand in newsvendor models:The case of singly truncated normal samples

Author

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  • Halkos, George
  • Kevork, Ilias

Abstract

This paper considers the classical newsvendor model when demand is normally distributed but with a large coefficient of variation. This leads to observe with a non-negligible probability negative values that do not make sense. To avoid the occurrence of such negative values, first, we derive generalized forms for the optimal order quantity and the maximum expected profit using properties of singly truncated normal distributions. Since truncating at zero produces non-symmetric distributions for the positive values, three alternative models are used to develop confidence intervals for the true optimal order quantity and the true maximum expected profit under truncation. The first model assumes traditional normality without truncation, while the other two models assume that demand follows (a) the log-normal distribution and (b) the exponential distribution. The validity of confidence intervals is tested through Monte-Carlo simulations, for low and high profit products under different sample sizes and alternative values for coefficient of variation. For each case, three statistical measures are computed: the coverage, namely the estimated actual confidence level, the relative average half length, and the relative standard deviation of half lengths. Only for very few cases the normal and the log-normal model produce confidence intervals with acceptable coverage but these intervals are characterized by low precision and stability.

Suggested Citation

  • Halkos, George & Kevork, Ilias, 2011. "Non-negative demand in newsvendor models:The case of singly truncated normal samples," MPRA Paper 31842, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:31842
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    File URL: https://mpra.ub.uni-muenchen.de/31842/1/MPRA_paper_31842.pdf
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    References listed on IDEAS

    as
    1. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, vol. 27(5), pages 537-553, October.
    2. David J. Braden & Marshall Freimer, 1991. "Informational Dynamics of Censored Observations," Management Science, INFORMS, vol. 37(11), pages 1390-1404, November.
    3. Strijbosch, L.W.G. & Moors, J.J.A., 2006. "Modified normal demand distributions in (R, S)-inventory control," European Journal of Operational Research, Elsevier, vol. 172(1), pages 201-212, July.
    4. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, vol. 38(3-4), pages 218-227, June.
    5. Bebu, Ionut & Mathew, Thomas, 2009. "Confidence intervals for limited moments and truncated moments in normal and lognormal models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 375-380, February.
    6. Maurice E. Schweitzer & GĂ©rard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
    7. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, vol. 98(3), pages 555-562, May.
    8. Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, vol. 100(3), pages 557-561, August.
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    Cited by:

    1. Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand," MPRA Paper 39650, University Library of Munich, Germany.
    2. Halkos, George & Kevork, Ilias, 2012. "The classical newsvendor model under normal demand with large coefficients of variation," MPRA Paper 40414, University Library of Munich, Germany.

    More about this item

    Keywords

    Inventory Management; Newsvendor model; Truncated normal; Demand estimation; Confidence intervals; Monte-Carlo simulations;

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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