Robust knapsack ordering for a partially-informed newsvendor with budget constraint

Abstract

This paper studies the multi-item newsvendor problem with a constrained budget and information about demand limited to its range, mean and mean absolute deviation. We consider a minimax model that determines order quantities by minimizing the expected overage and underage costs for the worst-case demand distributions. The resulting optimization problem turns out to be solvable by a method reminiscent of the greedy algorithm that solves the continuous knapsack problem, purchasing items in order of marginal value. This method has lower computational complexity compared to directly solving the model and leads to a simple policy that (i) sorts items based on their marginal effect on the total cost and (ii) determines order quantities according to this ranking until the budget is spent.