A Multi-Item Inventory Model with Joint Backorder Criterion

This paper considers a one-period multi-item inventory model where the objective is to minimize a function of item backorders subject to a budget constraint. Two functions are considered: the sum of expected item backorders and an expected joint backorder criterion. A main result is a proof that the joint backorder criterion is convex for arbitrary, twice-differentiable demand distributions. The rest of the paper is devoted to comparing the solutions one obtains with the two criterion functions.