Halkos, George and Kevork, Ilias (2011): Nonnegative demand in newsvendor models:The case of singly truncated normal samples.

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Abstract
This paper considers the classical newsvendor model when demand is normally distributed but with a large coefficient of variation. This leads to observe with a nonnegligible probability negative values that do not make sense. To avoid the occurrence of such negative values, first, we derive generalized forms for the optimal order quantity and the maximum expected profit using properties of singly truncated normal distributions. Since truncating at zero produces nonsymmetric distributions for the positive values, three alternative models are used to develop confidence intervals for the true optimal order quantity and the true maximum expected profit under truncation. The first model assumes traditional normality without truncation, while the other two models assume that demand follows (a) the lognormal distribution and (b) the exponential distribution. The validity of confidence intervals is tested through MonteCarlo simulations, for low and high profit products under different sample sizes and alternative values for coefficient of variation. For each case, three statistical measures are computed: the coverage, namely the estimated actual confidence level, the relative average half length, and the relative standard deviation of half lengths. Only for very few cases the normal and the lognormal model produce confidence intervals with acceptable coverage but these intervals are characterized by low precision and stability.
Item Type:  MPRA Paper 

Original Title:  Nonnegative demand in newsvendor models:The case of singly truncated normal samples 
Language:  English 
Keywords:  Inventory Management; Newsvendor model; Truncated normal; Demand estimation; Confidence intervals; MonteCarlo simulations 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C44  Operations Research; Statistical Decision Theory C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables > C34  Truncated and Censored Models; Switching Regression Models C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General 
Item ID:  31842 
Depositing User:  Nickolaos Tzeremes 
Date Deposited:  26. Jun 2011 10:21 
Last Modified:  12. Feb 2013 20:45 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/31842 