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Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand

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  • Halkos, George
  • Kevork, Ilias

Abstract

This paper considers the classical Newsvendor model, also known as the Newsboy problem, with the demand to be fully observed and to follow in successive inventory cycles one of the Exponential, Rayleigh, and Log-Normal distributions. For each distribution, appropriate estimators for the optimal order quantity are considered, and their sampling distributions are derived. Then, through Monte-Carlo simulations, we evaluate the performance of corresponding exact and asymptotic confidence intervals for the true optimal order quantity. The case where normality for demand is erroneously assumed is also investigated. Asymptotic confidence intervals produce higher precision, but to attain equality between their actual and nominal confidence level, samples of at least a certain size should be available. This size depends upon the coefficients of variation, skewness and kurtosis. The paper concludes that having available data on the skewed demand for enough inventory cycles enables (i) to trace non-normality, and (ii) to use the right asymptotic confidence intervals in order the estimates for the optimal order quantity to be valid and precise.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36205.

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Date of creation: Jan 2012
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Handle: RePEc:pra:mprapa:36205

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Keywords: Inventory Control; Newsboy Problem; Skewed Demand; Exact and Asymptotic Confidence Intervals; Monte-Carlo Simulations;

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  1. Casimir, Rommert J., 2002. "The value of information in the multi-item newsboy problem," Omega, Elsevier, Elsevier, vol. 30(1), pages 45-50, February.
  2. 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.
  3. Ridder, A.A.N. & Laan, E. van der & Salomon, M., 1997. "How Larger Demand Variability may Lead to Lower Costs in the Newsvendor Problem," Discussion Paper, Tilburg University, Center for Economic Research 1997-31, Tilburg University, Center for Economic Research.
  4. Lee, Chih-Ming & Hsu, Shu-Lu, 2011. "The effect of advertising on the distribution-free newsboy problem," International Journal of Production Economics, Elsevier, Elsevier, vol. 129(1), pages 217-224, January.
  5. Jammernegg, Werner & Kischka, Peter, 2009. "Risk preferences and robust inventory decisions," International Journal of Production Economics, Elsevier, Elsevier, vol. 118(1), pages 269-274, March.
  6. Marcelo Olivares & Christian Terwiesch & Lydia Cassorla, 2008. "Structural Estimation of the Newsvendor Model: An Application to Reserving Operating Room Time," Management Science, INFORMS, INFORMS, vol. 54(1), pages 41-55, January.
  7. Jorge Ibarra-Salazar, 2005. "The Newsboy Model: Changes in Risk and Price," The Geneva Papers on Risk and Insurance Theory, Springer, Springer, vol. 30(1), pages 99-109, June.
  8. Dominey, M. J. G. & Hill, R. M., 2004. "Performance of approximations for compound Poisson distributed demand in the newsboy problem," International Journal of Production Economics, Elsevier, Elsevier, vol. 92(2), pages 145-155, November.
  9. Grubbström, Robert W., 2010. "The Newsboy problem when customer demand is a compound renewal process," European Journal of Operational Research, Elsevier, Elsevier, vol. 203(1), pages 134-142, May.
  10. Mostard, Julien & de Koster, Rene & Teunter, Ruud, 2005. "The distribution-free newsboy problem with resalable returns," International Journal of Production Economics, Elsevier, Elsevier, vol. 97(3), pages 329-342, September.
  11. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, INFORMS, vol. 46(3), pages 404-420, March.
  12. Matsuyama, Keisuke, 2006. "The multi-period newsboy problem," European Journal of Operational Research, Elsevier, Elsevier, vol. 171(1), pages 170-188, May.
  13. Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, Elsevier, vol. 37(1), pages 93-105, February.
  14. Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, Elsevier, vol. 100(3), pages 557-561, August.
  15. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, Elsevier, vol. 39(3), pages 302-312, June.
  16. Su, Rung Hung & Pearn, Wen Lea, 2011. "Product selection for newsboy-type products with normal demands and unequal costs," International Journal of Production Economics, Elsevier, Elsevier, vol. 132(2), pages 214-222, August.
  17. 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.
  18. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, Elsevier, vol. 98(3), pages 555-562, May.
  19. Chen, Liang-Hsuan & Chen, Ying-Che, 2010. "A multiple-item budget-constraint newsboy problem with a reservation policy," Omega, Elsevier, Elsevier, vol. 38(6), pages 431-439, December.
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