Optimal and heuristic solutions for the multi-item newsvendor problem with a single capacity constraint

This research considers a multi-item newsvendor problem with a single capacity constraint. While this problem has been addressed in the literature, the focus here is on developing simple, closed-form expressions for the order quantities. The benefit of such an approach is that the solutions are straightforward to calculate and have managerial appeal. Additionally, we show these expressions to be optimal under a variety of conditions. For more general cases when these optimality conditions do not hold, we use these expressions as heuristic solutions. Via computational studies, we demonstrate that these heuristics are extremely effective when the optimality conditions are not satisfied.