Halkos, George and Kevork, Ilias (2012): The classical newsvendor model under normal demand with large coefficients of variation.

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Abstract
In 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 stockout 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.
Item Type:  MPRA Paper 

Original Title:  The classical newsvendor model under normal demand with large coefficients of variation 
Language:  English 
Keywords:  Classical newsvendor model; truncated normal distribution; optimality condition; critical fractile; loss of goodwill; relative approximation error 
Subjects:  M  Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M1  Business Administration > M11  Production Management C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research ; Statistical Decision Theory C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C24  Truncated and Censored Models ; Switching Regression Models ; Threshold Regression Models M  Business Administration and Business Economics ; Marketing ; Accounting ; Personnel Economics > M2  Business Economics > M21  Business Economics 
Item ID:  40414 
Depositing User:  G.E. Halkos 
Date Deposited:  01. Aug 2012 18:32 
Last Modified:  22. Aug 2015 15:11 
References:  Benzion, U., Cohen, Y., Peled, R., Shavit, T. (2008). Decision making and the newsvendor problem: an experimental study. Journal of the Operational Research Society 59: 12811287. Benzion, U., Cohen, Y., Shavit, T. (2010). The newsvendor problem with unknown distribution. Journal of the Operational Research Society 61: 10221031. Gallego, G., Katircioglu, K., Ramachandran, B. (2007). Inventory management under highly uncertain demand. Operations Research Letters 35: 281289. Halkos, G.E., Kevork, I.S. (2011). Nonnegative demand in newsvendor models: The case of singly truncated normal samples. MPRA Paper No. 31842, Online at http://mpra.ub.unimuenchen.de/31842/. Hu, J., Munson, C.L. (2011). Improved profit functions for newsvendor models with normally distributed demand. International Journal of Procurement Management 4: 2036. Janssen, E., Strijbosch, L., Brekelmans, R. (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 118: 3442. Johnson, N.L., S. Kotz, N, Bakakrishnan. 1994. Continuous Univariate Distributions. Vol. 1, 2nd Edition. Wiley New York. Kevork, I.S. (2010). Estimating the optimal order quantity and the maximum expected profit for singleperiod inventory decisions. Omega 38: 218–27. Khouja, M. (1999). The singleperiod (newsvendor) problem: literature review and suggestions for future research. Omega 27:537–53. Lapin, L.L. (1994). Quantitative methods for business decision with cases, 6th ed. Duxbury Press, An International Thomson Publishing Company. Lau, H. (1997). Simple Formulas for the Expected Costs in the Newsboy Problem: an educational note. European Journal of Operational Research 100: 557–61. Perakis, G., Roels, G. (2008). Regret in the newsvendor model with partial information. Operations Research 56: 188203. Schweitzer, M.E., Cachon, G.P. (2000). Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence. Management Science 46: 404–420. Silver, E.A., Pyke, D.F., Peterson, R. (1998). Inventory management and production planning and scheduling, 3rd ed. New York, NY: John Wiley & Sons. Steinbrecher, G., Shaw, W.T. (2008). Quantile mechanics. European Journal of Applied Mathematics 19: 87112. Strijbosch, L.W.G., Moors, J.J.A. (2006). Modified normal demand distributions in (R,S)inventory control. European Journal of Operational Research 172: 201212. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/40414 