Polyhedral Results and Branch-and-Cut for the Resource Loading Problem

We study the resource loading problem, which arises in tactical capacity planning. In this problem, one has to plan the intensity of execution of a set of orders to minimize a cost function that penalizes the resource use above given capacity limits and the completion of the orders after their due dates. Our main contributions include a novel mixed-integer linear-programming (MIP)‐based formulation, the investigation of the polyhedra associated with the feasible intensity assignments of individual orders, and a comparison of our branch-and-cut algorithm based on the novel formulation and the related polyhedral results with other MIP formulations. The computational results demonstrate the superiority of our approach. In our formulation and in one of the proofs, we use fundamental results of Egon Balas on disjunctive programming.