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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36460.

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Date of creation: Feb 2012
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Handle: RePEc:pra:mprapa:36460

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Keywords: Inventory Control; Classical newsvendor model; Exponential and Rayleigh Distributions; Confidence Intervals; Monte-Carlo Simulations;

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References

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  1. Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, vol. 37(1), pages 93-105, February.
  2. Lee, Chih-Ming & Hsu, Shu-Lu, 2011. "The effect of advertising on the distribution-free newsboy problem," International Journal of Production Economics, Elsevier, vol. 129(1), pages 217-224, January.
  3. 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.
  4. Marcelo Olivares & Christian Terwiesch & Lydia Cassorla, 2008. "Structural Estimation of the Newsvendor Model: An Application to Reserving Operating Room Time," Management Science, INFORMS, vol. 54(1), pages 41-55, January.
  5. Huang, Di & Zhou, Hong & Zhao, Qiu-Hong, 2011. "A competitive multiple-product newsboy problem with partial product substitution," Omega, Elsevier, vol. 39(3), pages 302-312, June.
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  7. Casimir, Rommert J., 2002. "The value of information in the multi-item newsboy problem," Omega, Elsevier, vol. 30(1), pages 45-50, February.
  8. Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
  9. 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.
  10. Hill, Roger M., 1997. "Applying Bayesian methodology with a uniform prior to the single period inventory model," European Journal of Operational Research, Elsevier, vol. 98(3), pages 555-562, May.
  11. Jorge Ibarra-Salazar, 2005. "The Newsboy Model: Changes in Risk and Price," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 30(1), pages 99-109, June.
  12. Chen, Liang-Hsuan & Chen, Ying-Che, 2010. "A multiple-item budget-constraint newsboy problem with a reservation policy," Omega, Elsevier, vol. 38(6), pages 431-439, December.
  13. Jammernegg, Werner & Kischka, Peter, 2009. "Risk preferences and robust inventory decisions," International Journal of Production Economics, Elsevier, vol. 118(1), pages 269-274, March.
  14. 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, vol. 132(2), pages 214-222, August.
  15. Grubbström, Robert W., 2010. "The Newsboy problem when customer demand is a compound renewal process," European Journal of Operational Research, Elsevier, vol. 203(1), pages 134-142, May.
  16. Matsuyama, Keisuke, 2006. "The multi-period newsboy problem," European Journal of Operational Research, Elsevier, vol. 171(1), pages 170-188, May.
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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, 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.

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