Uncertain random newsboy problem

The classic newsboy problem assumes the market demand to be a random variable. However, when the decision maker wants to expand the market share, he has to provide a subjective estimate of new market demand distribution due to the lack of historical data. Thus, randomness and uncertainty simultaneously appear in a newsboy problem. The aim of this work is to extend the analysis of the classic newsboy problem to the case when market demand is assumed to be an uncertain random variable. A mathematical model is formulated, and a simple equation is derived for determining the optimal order quantity to maximize the expected profit. Furthermore, uncertain random newsboy problem is compared with stochastic newsboy problem and uncertain newsboy problem. Three kinds of newsboy problems have the same optimal service level. The latter two newsboy problems are two special cases of uncertain random newsboy problem. Finally, a numerical example has been presented to illustrate the model.