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Evaluating alternative frequentist inferential approaches for optimal order quantities in the newsvendor model under exponential demand

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  • Halkos, George
  • Kevork, Ilias

Abstract

Three estimation policies for the optimal order quantity of the classical newsvendor model under exponential demand are evaluated in the current paper. According to the principle of the first estimation policy, the corresponding estimator is obtained replacing in the theoretical formula which gives the optimal order quantity the parameter of exponential distribution with its maximum likelihood estimator. The estimator of the second estimation policy is derived in such a way as to ensure that the requested critical fractile is attained. For the third estimation policy, the corresponding estimator is obtained maximizing the a-priori expected profit with respect to a constant which has been included into the form of the estimator. Three statistical measures have been chosen to perform the evaluation. The actual critical fractile attained by each estimator, the mean square error, and the range of deviation of estimates from the optimal order quantity, when the probability to take such a range is the same for the three estimation policies. The behavior of the three statistical measures is explored under different combinations of sample sizes and critical fractiles. With small sample sizes, no estimation policy predominates over the others. The estimator which attains the closest actual critical fractile to the requested one, this estimator has the largest mean square and the largest range of deviation of estimates from the optimal order quantity. On the contrary, with samples over 40 observations, the choice is restricted among the estimators of the first and third estimation policy. To facilitate this choice, at different sample sizes, we offer the required values of the critical fractile which determine which estimation policy eventually should be applied.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:39650
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Halkos, George & Kevork, Ilias, 2014. "Διαστήματα Εμπιστοσύνης Για Εκατοστημόρια Σε Στάσιμες Arma Διαδικασίες: Μία Εμπειρική Εφαρμογή Σε Περιβαλλοντικά Δεδομένα [Confidence intervals for percentiles in stationary ARMA processes: An appl," MPRA Paper 56134, University Library of Munich, Germany.
    3. 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.

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    More about this item

    Keywords

    Classical newsvendor model; Exponential distribution; Demand estimation; Actual critical fractile; Mean square error of estimators;
    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
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity

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