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The classical newsvendor model under normal demand with large coefficients of variation

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  • Halkos, George
  • Kevork, Ilias

Abstract

In the classical newsvendor model, when demand is represented by the normal distribution singly truncated at point zero, the standard optimality condition does not hold. Particularly, we show that the probability not to have stock-out during the period is always greater than the critical fractile which depends upon the overage and the underage costs. For this probability we derive the range of its values. Writing the safety stock coefficient as a quantile function of both the critical fractile and the coefficient of variation we obtain appropriate formulae for the optimal order quantity and the maximum expected profit. These formulae enable us to study the changes of the two target inventory measures when the coefficient of variation increases. For the optimal order quantity, the changes are studied for different values of the critical fractile. For the maximum expected profit, its changes are examined for different combinations of the critical fractile and the loss of goodwill. The range of values for the loss of goodwill ensures that maximum expected profits are positive. The sizes of the relative approximation error which result in by using the normal distribution to compute the optimal order quantity and the maximum expected profit are also investigated. This investigation is extended to different values of the critical fractile and the loss of goodwill. The results indicate that it is naïve to suggest for the coefficient of variation a maximum flat value under which the normal distribution approximates well the target inventory measures.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:40414
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    References listed on IDEAS

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    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. U Benzion & Y Cohen & R Peled & T Shavit, 2008. "Decision-making and the newsvendor problem: an experimental study," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(9), pages 1281-1287, September.
    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. 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.
    6. Maurice E. Schweitzer & Gérard 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. Janssen, Elleke & Strijbosch, Leo & Brekelmans, Ruud, 2009. "Assessing the effects of using demand parameters estimates in inventory control and improving the performance using a correction function," International Journal of Production Economics, Elsevier, vol. 118(1), pages 34-42, March.
    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, 2013. "Forecasting the optimal order quantity in the newsvendor model under a correlated demand," MPRA Paper 44189, University Library of Munich, Germany.
    2. Halkos, George & Kevork, Ilias, 2012. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.

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    More about this item

    Keywords

    Classical newsvendor model; truncated normal distribution; optimality condition; critical fractile; loss of goodwill; relative approximation error;
    All these keywords.

    JEL classification:

    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics

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