On Solving the Maximum Flow Problem with Conflict Constraints

The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches, both heuristic and exact, have been proposed to attack the problem.In this paper we consider a mixed integer linear program and solve it with an open-source solver. Computational results on the benchmark instances commonly used in the literature of the problem are reported. All the 160 instances benchmark instances normally used in the literature are solved to optimality for the first time, with 28 instances closed for the first time. Moreover, in the process, 6 improvements to the best-known heuristic solutions are also found.