Robustness analysis of stochastic inventory systems using the newsboy model

What is the best quantity of a given good that we can buy today for selling tomorrow? Obviously, the answer depends on the knowledge we have about the future trends of the market. When expressing this knowledge by a probability distribution, many assumptions are often introduced that are not founded on actual knowledge, but only on computational ease. In this paper, we examine how robust are decisions taken from this kind of limited knowledge. For that we use the framework of the newsboy model and the attached Scarf's theorem, that assumes the knowledge of both the mean and the standard deviation. We also obtain new results for the max–min problem against the family of triangular distributions. This family is of practical interest since its parameters are the mode and the range of the demand. Moreover, a new measure of the dispersion, the intermeans parameter is introduced. Assuming the knowledge of both the mean and this new parameter leads to new situations and a partial result has been obtained. Our assertions are illustrated by numerical examples, and the information value of the various assumptions are observed.