Non-negative demand in newsvendor models:The case of singly truncated normal samples
AbstractThis paper considers the classical newsvendor model when demand is normally distributed but with a large coefficient of variation. This leads to observe with a non-negligible 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 non-symmetric 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 log-normal distribution and (b) the exponential distribution. The validity of confidence intervals is tested through Monte-Carlo 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 log-normal model produce confidence intervals with acceptable coverage but these intervals are characterized by low precision and stability.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 31842.
Date of creation: 2011
Date of revision:
Inventory Management; Newsvendor model; Truncated normal; Demand estimation; Confidence intervals; Monte-Carlo simulations;
Find related papers by JEL classification:
- C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
- C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-07-02 (All new papers)
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