Exact and heuristic algorithms for the interval min-max regret generalized assignment problem

We consider the generalized assignment problem (GAP) with min-max regret criterion under interval costs. This problem models many real-world applications in which jobs must be assigned to agents but the costs of assignment may vary after the decision has been taken. We computationally examine two heuristic methods: a fixed-scenario approach and a dual substitution algorithm. We also examine exact algorithmic approaches (Benders-like decomposition and branch-and-cut) and further introduce a more sophisticated algorithm that incorporates various methodologies, including Lagrangian relaxation and variable fixing. The resulting Lagrangian-based branch-and-cut algorithm performs satisfactorily on benchmark instances.