A combinatorial relaxation methodology for berth allocation problems

We investigate an optimization problem in container ports, for which previous models based on generalized set partitioning formulations have been studied. We describe two combinatorial relaxations based on computing maximum weighted matchings in suitable graphs. Besides dual bounds, those also provide a variable reduction technique and a matheuristic. Computational results indicate that the algorithm is an efficient alternative capable of finding the known optimal solutions on 83% of the benchmark instances. Even in the most difficult set of instances, solutions within 4% of the optimal value are provided, with an average of 30% of the time required by methods previously described in the literature.