The robust maximum-coverage problem

The maximum coverage problem is a staple of facility location theory, and has more recently been extended to the covering facility interdiction problem, in which covering facilities are chosen for interdiction so as to minimize the resultant coverage. This paper considers the opposite to the interdiction problem, selecting facilities to maximize coverage after the worst-case interdiction. Solutions to this problem would inform facility placement when intentional disruption is feared, or when guaranteeing minimum coverages in the presence of random facility outages. Several approaches to the problem are considered, primarily derivatives of approaches to the structurally similar maximum coverage problem. An integer linear program formulation proves infeasible for problems of even modest size, despite exclusion of many non-binding constraints, but heuristic approaches (again adaptations of maximum coverage heuristics) show promise in both efficiency and solutions quality.