A Note on Mean-variance Analysis of the Newsvendor Model with Stockout Cost

We apply the mean-variance approach to analyze the risk-averse newsvendor problem with stockout cost. We first derive an explicit form and some new properties of the variance of the profit function. Then, under the assumption that demand follows the power distribution, and its special case the uniform distribution, we obtain the set of optimal ordering quantities. We also give a counterexample to one result presented in the literature. Contrary to the traditional result in the literature that the risk-averse newsvendor always orders less than the risk-neutral newsvendor, our findings show that this may not be the case when stockout cost is considered because the newsvendor may order more than the risk-neutral newsvendor order quantity under a stockout situation with mean-variance tradeoff.