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Forecasting the optimal order quantity in the newsvendor model under a correlated demand

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  • Halkos, George
  • Kevork, Ilias

Abstract

This paper considers the classical newsvendor model when, (a) demand is autocorrelated, (b) the parameters of the marginal distribution of demand are unknown, and (c) historical data for demand are available for a sample of successive periods. An estimator for the optimal order quantity is developed by replacing in the theoretical formula which gives this quantity the stationary mean and the stationary variance with their corresponding maximum likelihood estimators. The statistical properties of this estimator are explored and general expressions for prediction intervals for the optimal order quantity are derived in two cases: (a) when the sample consists of two observations, and (b) when the sample is considered as sufficiently large. Regarding the asymptotic prediction intervals, specifications of the general expression are obtained for the time-series models AR(1), MA(1), and ARMA(1,1). These intervals are estimated in finite samples using in their theoretical expressions, the sample mean, the sample variance, and estimates of the theoretical autocorrelation coefficients at lag one and lag two. To assess the impact of this estimation procedure on the optimal performance of the newsvendor model, four accuracy implication metrics are considered which are related to: (a) the mean square error of the estimator, (b) the accuracy and the validity of prediction intervals, and (c) the actual probability of running out of stock during the period when the optimal order quantity is estimated. For samples with more than two observations, these metrics are evaluated through simulations, and their values are presented to appropriately constructed tables. The general conclusion is that the accuracy and the validity of the estimation procedure for the optimal order quantity depends upon the critical fractile, the sample size, the autocorrelation level, and the convergence rate of the theoretical autocorrelation function to zero.

Suggested Citation

  • 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.
  • Handle: RePEc:pra:mprapa:44189
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    File URL: https://mpra.ub.uni-muenchen.de/44189/1/MPRA_paper_44189.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. Zhang, Xiaolong, 2007. "Inventory control under temporal demand heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 182(1), pages 127-144, October.
    3. John Boylan & Aris Syntetos, 2006. "Accuracy and Accuracy Implication Metrics for Intermittent Demand," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, issue 4, pages 39-42, June.
    4. 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.
    5. 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.
    6. G. D. Johnson & H. E. Thompson, 1975. "Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes," Management Science, INFORMS, vol. 21(11), pages 1303-1307, July.
    7. Fotopoulos, Stergios & Wang, Min-Chiang & Rao, S. Subba, 1988. "Safety stock determination with correlated demands and arbitrary lead times," European Journal of Operational Research, Elsevier, vol. 35(2), pages 172-181, May.
    8. 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.
    9. Urban, Timothy L., 2005. "A periodic-review model with serially-correlated, inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 95(3), pages 287-295, March.
    10. Strijbosch, Leo W.G. & Syntetos, Aris A. & Boylan, John E. & Janssen, Elleke, 2011. "On the interaction between forecasting and stock control: The case of non-stationary demand," International Journal of Production Economics, Elsevier, vol. 133(1), pages 470-480, September.
    11. Syntetos, Aris A. & Nikolopoulos, Konstantinos & Boylan, John E., 2010. "Judging the judges through accuracy-implication metrics: The case of inventory forecasting," International Journal of Forecasting, Elsevier, vol. 26(1), pages 134-143, January.
    12. 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.
    13. Alp Akcay & Bahar Biller & Sridhar Tayur, 2011. "Improved Inventory Targets in the Presence of Limited Historical Demand Data," Manufacturing & Service Operations Management, INFORMS, vol. 13(3), pages 297-309, July.
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    Citations

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    Cited by:

    1. 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.

    More about this item

    Keywords

    Newsvendor model; accuracy implication metrics; time-series models; prediction intervals; Monte-Carlo simulations;

    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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • M21 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - Business Economics

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