A Branch-and-Benders-Cut Approach to Solve the Maximum Flow Blocker Problem

Given a directed graph with capacities and interdiction costs associated with its arcs, the maximum flow blocker problem (MFBP) asks to find a minimum-cost subset of arcs to be removed from the graph in such a way that the remaining maximum-flow value does not exceed a given threshold. The MFBP has applications in telecommunication networks and in the monitoring of civil infrastructures, among others. We propose an integer linear programming formulation (ILP) with an exponential number of constraints, called Benders cut, for the MFBP. Accordingly, we derive a branch-and-cut algorithm to optimally solve the problem. Preliminary experimental results are reported to assess performance of the formulation and more precisely to determine the dimension of the problem that could be solved to proven optimality.