The distribution-free newsboy problem and the demand skew

We consider the newsboy problem when the information about the probability distribution of random demand is limited to its support, mean, variance, and skewness. Sharp lower and upper bounds on the maximum expected profit are derived that lead to the corresponding optimal order quantities found under the worst-case and best-case scenarios. In addition, some special cases are solved by reducing the scope of knowledge about the demand distribution. Consequently, we generalize all results presented so far in the literature for the two scenarios, and present several new results. A numerical example illustrates the impact of available information on the quality of approximations. Extensions of our results are indicated.