Uncertain multi-product newsboy problem with chance constraint

• A new uncertain multi-product newsboy model based on uncertainty theory is modelled.
• It is proved that there exists an equivalence relation between the uncertain multi-product newsboy model and a deterministic integer programming model.
• Three numerical examples were given to illustrate how to use the proposed model to make ordering policy.

A multi-product newsboy problem with uncertain demand and uncertain storage space is investigated under a warehousing chance constraint. It is assumed that indeterminacy may appear in demand and storage space due to rough estimation of their distributions by decision-maker. Uncertainty theory provides a new tool to deal with the human uncertainty. We develop an uncertain expected value programming model (UEVPM) based on uncertainty theory. Uncertain variables (functions from uncertainty space to the set of real numbers) are used to describe subjective estimation. The objective function is to maximize the expected profit of newsboy at a predetermined confidence level. Furthermore, we convert the chance constrained uncertain programming model to its equivalent deterministic form so as to be solved by classic integer programming method. Finally, three numerical examples are given to illustrate the potential usefulness of the study.