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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 44189.

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Date of creation: 04 Feb 2013
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Handle: RePEc:pra:mprapa:44189

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

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References

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  1. 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, Elsevier, vol. 35(2), pages 172-181, May.
  2. Alp Akcay & Bahar Biller & Sridhar Tayur, 2011. "Improved Inventory Targets in the Presence of Limited Historical Demand Data," Manufacturing & Service Operations Management, INFORMS, INFORMS, vol. 13(3), pages 297-309, July.
  3. 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, Elsevier, vol. 118(1), pages 34-42, March.
  4. Kevork, Ilias S., 2010. "Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions," Omega, Elsevier, Elsevier, vol. 38(3-4), pages 218-227, June.
  5. Khouja, Moutaz, 1999. "The single-period (news-vendor) problem: literature review and suggestions for future research," Omega, Elsevier, Elsevier, vol. 27(5), pages 537-553, October.
  6. John Boylan & Aris Syntetos, 2006. "Accuracy and Accuracy Implication Metrics for Intermittent Demand," Foresight: The International Journal of Applied Forecasting, International Institute of Forecasters, International Institute of Forecasters, issue 4, pages 39-42, June.
  7. 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.
  8. Zhang, Xiaolong, 2007. "Inventory control under temporal demand heteroscedasticity," European Journal of Operational Research, Elsevier, Elsevier, vol. 182(1), pages 127-144, October.
  9. Urban, Timothy L., 2005. "A periodic-review model with serially-correlated, inventory-level-dependent demand," International Journal of Production Economics, Elsevier, Elsevier, vol. 95(3), pages 287-295, March.
  10. G. D. Johnson & H. E. Thompson, 1975. "Optimality of Myopic Inventory Policies for Certain Dependent Demand Processes," Management Science, INFORMS, INFORMS, vol. 21(11), pages 1303-1307, July.
  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, Elsevier, vol. 26(1), pages 134-143, January.
  12. 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, Elsevier, vol. 133(1), pages 470-480, September.
  13. 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.
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Cited by:
  1. Halkos, George & Kevork, Ilias, 2014. "Διαστήματα Εμπιστοσύνης Για Εκατοστημόρια Σε Στάσιμες Arma Διαδικασίες: Μία Εμπειρική Εφαρμογή Σε Περιβαλλον�," MPRA Paper 56134, University Library of Munich, Germany.

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