How larger demand variability may lead to lower costs in the Newsboy Problem

Intuition may lead to the hypothesis that in stochastic inventory systems a higher demand variability results in larger variances and in an increase of total expected system costs. In a recent paper, Song [5] formally proved this assertion to hold for a certain class of inventory models (including the Newsboy Problem), given a particular definition of variability. Here we use stochastic dominance relations in the Newsboy Problem to characterize demand distributions for which the opposite effect may occur, i.e., higher demand variability may result in larger variances and lower costs. In addition, we provide necessary and sufficient conditions under which larger demand variances and lower costs occur simultaneously.