Bipartite complete matching vertex interdiction problem with incompatibility constraints: Complexity and heuristics

In this paper, we consider the bipartite complete matching vertex interdiction problem, taking into account some incompatibilities existing among the resources to assign. This problem ensures the obtainment of a robust assignment, which is defined by the number of missing resources still allowing a valid assignment. We introduce graph formulations, considering a single time period or several ones. This problem is shown to be NP-hard, even when considering only a single time period. For several time periods, we adapt the graph formulation, allowing us to solve the problem using polynomial heuristics. Two greedy algorithms and a genetic algorithm are proposed and compared on a randomly-generated testbed.