This research proposes and analyzes new models for a stochastic resource allocation problem that arises in a variety of operations contexts. One of the primary contributions of the paper lies in providing a succinct, robust, and general model that can address a range of different risk-based objectives and cost assumptions under uncertainty. Although the model expression is relatively simple, it embeds a reasonably high degree of underlying complexity, as the analysis shows. In addition, in-depth analysis of the model, both in its general form and under various specific risk measures, uncovers some interesting and powerful insights regarding the problem trade-offs. Furthermore, this analysis leads to a highly efficient class of heuristic algorithms for solving the problem, which we demonstrate via numerical experimentation to provide close-to-optimal solutions. This computational benefit is a critical element for solving a class of broadly applicable larger problems for which our problem arises as a subproblem that requires repeated solution.

This paper considers a very general class of customer-to-resource assignment problems relevant to a variety of manufacturing contexts. This problem class addresses settings in which subsets of customer types share resource capacities as well as a fixed amount of capacity consumption, independent of production volume. More broadly, our model addresses cross-facility production limits and shared capacity consumption within each customer type. To solve these large-scale optimization problems, we apply a branch-and-price solution approach. This approach relies on an effective solution method for a novel class of nonlinear knapsack pricing problems. As our computational results demonstrate, despite the fact that the resulting master problem is not a simple set-partitioning problem, the problem's relaxation is sufficiently tight to produce an algorithm that significantly outperforms CPLEX for a wide range of problem parameter settings.