The classical newsvendor model under normal demand with large coefficients of variation
AbstractIn the classical newsvendor model, when demand is represented by the normal distribution singly truncated at point zero, the standard optimality condition does not hold. Particularly, we show that the probability not to have stock-out during the period is always greater than the critical fractile which depends upon the overage and the underage costs. For this probability we derive the range of its values. Writing the safety stock coefficient as a quantile function of both the critical fractile and the coefficient of variation we obtain appropriate formulae for the optimal order quantity and the maximum expected profit. These formulae enable us to study the changes of the two target inventory measures when the coefficient of variation increases. For the optimal order quantity, the changes are studied for different values of the critical fractile. For the maximum expected profit, its changes are examined for different combinations of the critical fractile and the loss of goodwill. The range of values for the loss of goodwill ensures that maximum expected profits are positive. The sizes of the relative approximation error which result in by using the normal distribution to compute the optimal order quantity and the maximum expected profit are also investigated. This investigation is extended to different values of the critical fractile and the loss of goodwill. The results indicate that it is naïve to suggest for the coefficient of variation a maximum flat value under which the normal distribution approximates well the target inventory measures.
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.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 40414.
Date of creation: Aug 2012
Date of revision:
Classical newsvendor model; truncated normal distribution; optimality condition; critical fractile; loss of goodwill; relative approximation error;
Find related papers by JEL classification:
- M11 - Business Administration and Business Economics; Marketing; Accounting - - Business Administration - - - Production Management
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
- C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models
- M21 - Business Administration and Business Economics; Marketing; Accounting - - Business Economics - - - Business Economics
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-08-23 (All new papers)
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.:
- 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.
- 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.
- 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.
- 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.
- Strijbosch, L.W.G. & Moors, J.J.A., 2006. "Modified normal demand distributions in (R, S)-inventory control," European Journal of Operational Research, Elsevier, Elsevier, vol. 172(1), pages 201-212, July.
- Uri Ben-Zion & Yuval Cohen & Ruth Peled & TAL SHAVIT, 2007. "Decision-Making and the Newsvendor Problem – An Experimental Study," Working Papers, Ben-Gurion University of the Negev, Department of Economics 0711, Ben-Gurion University of the Negev, Department of Economics.
- 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.
- 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.
- 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, 2013. "Forecasting the optimal order quantity in the newsvendor model under a correlated demand," MPRA Paper 44189, University Library of Munich, Germany.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
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.