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Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand

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  • Halkos, George
  • Kevork, Ilias

Abstract

In this paper we consider the classical newsvendor model with profit maximization. When demand is fully observed in each period and follows either the Rayleigh or the exponential distribution, appropriate estimators for the optimal order quantity and the maximum expected profit are established and their distributions are derived. Measuring validity and precision of the corresponding generated confidence intervals by respectively the actual confidence level and the expected half-length divided by the true quantity (optimal order quantity or maximum expected profit), we prove that the intervals are characterized by a very important and useful property. Either referring to confidence intervals for the optimal order quantity or the maximum expected profit, measurements for validity and precision take on exactly the same values. Furthermore, validity and precision do not depend upon the values assigned to the revenue and cost parameters of the model. To offer, therefore, a-priori knowledge for levels of precision and validity, values for the two statistical criteria, that is, the actual confidence level and the relative expected half-length are provided for different combinations of sample size and nominal confidence levels 90%, 95% and 99%. The values for the two criteria have been estimated by developing appropriate Monte-Carlo simulations. For the relative-expected half-length, values are computed also analytically.

Suggested Citation

  • Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:36460
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    References listed on IDEAS

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    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. "Unbiased estimation of maximum expected profits in the Newsvendor Model: a case study analysis," MPRA Paper 40724, University Library of Munich, Germany.
    3. Rung-Hung Su & Dong-Yuh Yang & He-Jhen Lin & Yu-Cheng Yang, 2023. "Estimating conservative profitability of a newsboy-type product with exponentially distributed demand based on multiple samples," Annals of Operations Research, Springer, vol. 322(2), pages 967-989, March.
    4. Rung-Hung Su & Chia-Ding Hou & Jou-Yu Lee, 2024. "Obtaining Conservative Estimates of Integrated Profitability for a Single-Period Product in an Own-Branding-and-Manufacturing Enterprise with Multiple Owned Channels," Mathematics, MDPI, vol. 12(13), pages 1-19, July.

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    More about this item

    Keywords

    Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo Simulations;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • 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
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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