Vessel scheduling with pilotage and tugging considerations

This paper considers vessel scheduling with pilotage and tugging constraints in berthing operations with channel restrictions at seaports. To our knowledge, pilotage and tugging requirements have not been simultaneously considered in the literature. This work proposes a mixed integer programming (MIP) formulation and an exact solution approach, based on constraint separation techniques, to solve the problem. The solution approach is initiated with a heuristic that runs in polynomial time. The approach then adds separation cuts to a relaxed version of the MIP formulation and updates the bounds until an optimal solution has been found. A real case and simulated realistic cases are used to compare the proposed model against the first-come first-serve (FCFS) policy that is traditionally used in vessel scheduling. The results show that significant improvements can be obtained, especially during congestion periods. Finally, a computational study demonstrates that the proposed solution approach is capable of solving real-size cases in a reasonable time.