Estimating the optimal order quantity and the maximum expected profit for single-period inventory decisions
AbstractThe paper considers the classical single-period inventory model, also known as the Newsboy Problem, with the demand normally distributed and fully observed in successive inventory cycles. The extent of applicability of such a model to inventory management depends upon demand estimation. Appropriate estimators for the optimal order quantity and the maximum expected profit are developed. The statistical properties of the two estimators are explored for both small and large samples, analytically and through Monte-Carlo simulations. For small samples, both estimators are biased. The form of distribution of the optimal order quantity estimator depends upon the critical fractile, while the distribution of the maximum expected profit estimator is always left-skewed. Small samples properties of the estimators indicate that, when the critical fractile is set over a half, the optimal order quantity is underestimated and the maximum expected profit is overestimated with probability over 50%, whereas the probability of overestimating both quantities exceeds again 50% when the critical fractile is below a half. For large samples, based on the asymptotic properties of the two estimators, confidence intervals are derived for the corresponding true population values. The validity of confidence intervals using small samples is tested by developing appropriate Monte-Carlo simulations. In small samples, these intervals attain acceptable confidence levels, but with high unit shortage cost, for the case of maximum expected profit, significant reductions in their precision and stability are observed.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Omega.
Volume (Year): 38 (2010)
Issue (Month): 3-4 (June)
Contact details of provider:
Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/375/description#description
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wang, Charles X. & Webster, Scott, 2009. "The loss-averse newsvendor problem," Omega, Elsevier, vol. 37(1), pages 93-105, February.
- 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.
- Wu, Jun & Li, Jian & Wang, Shouyang & Cheng, T.C.E., 2009. "Mean-variance analysis of the newsvendor model with stockout cost," Omega, Elsevier, vol. 37(3), pages 724-730, June.
- Berk, Emre & Gurler, Ulku & Levine, Richard A., 2007. "Bayesian demand updating in the lost sales newsvendor problem: A two-moment approximation," European Journal of Operational Research, Elsevier, vol. 182(1), pages 256-281, October.
- David Goldsman & Lee Schruben, 1984. "Asymptotic Properties of Some Confidence Interval Estimators for Simulation Output," Management Science, INFORMS, vol. 30(10), pages 1217-1225, October.
- 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.
- Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
- Lau, Hon-Shiang & Hing-Ling Lau, Amy, 1996. "Estimating the demand distributions of single-period items having frequent stockouts," European Journal of Operational Research, Elsevier, vol. 92(2), pages 254-265, July.
- Hon-Shiang Lau, 1997. "Simple formulas for the expected costs in the newsboy problem: An educational note," European Journal of Operational Research, Elsevier, vol. 100(3), pages 557-561, August.
- Chahar, Kiran & Taaffe, Kevin, 2009. "Risk averse demand selection with all-or-nothing orders," Omega, Elsevier, vol. 37(5), pages 996-1006, October.
- 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.
- 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.
- 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.
- Halkos, George & Kevork, Ilias, 2011. "Non-negative demand in newsvendor models:The case of singly truncated normal samples," MPRA Paper 31842, University Library of Munich, Germany.
- 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.
- 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.
- Zhao, Li & Tian, Peng & Xiangyong Li, 2012. "Dynamic pricing in the presence of consumer inertia," Omega, Elsevier, vol. 40(2), pages 137-148, April.
- Halkos, George & Kevork, Ilias, 2012. "Validity and precision of estimates in the classical newsvendor model with exponential and rayleigh demand," MPRA Paper 36460, University Library of Munich, Germany.
- 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.
- Hsieh, Tsu-Pang & Dye, Chung-Yuan, 2012. "A note on "The EPQ with partial backordering and phase-dependent backordering rate"," Omega, Elsevier, vol. 40(1), pages 131-133, January.
- Khanra, Avijit & Soman, Chetan A., . "Sensitivity Analysis of the Newsboy Model," IIMA Working Papers WP2013-09-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
- 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.
- Halkos, George & Kevork, Ilias, 2012. "Evaluating alternative estimators for optimal order quantities in the newsvendor model with skewed demand," MPRA Paper 36205, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.