Approach Integrating Mixed-Integer Programming and Constraint Programming for Planning Rotations of Inland Vessels in a Large Seaport

During the past decade, inland vessels have gained importance in container transport because of their reliability, low environmental impact, and major capacity for increased exploitation. Although inland vessels are crucial in container transport between terminals in the port and the hinterland, in a large seaport like the one in Rotterdam, Netherlands, only 62% of the inland vessels leave the port on time. The other vessels have to stay in the port area for a longer time than planned. This situation leads to uncertainty in waiting times of vessels at terminals and low utilization of terminal quay resources. A two-phase approach is proposed that integrates mixed-integer programming (MIP) and constraint programming (CP) to solve the problem by generating optimal rotation plans for inland vessels. In the first phase, the single-vessel optimization problem is formulated on the basis of MIP and solved with state-of-the-art MIP solvers. In the second phase, the multiple-vessel coordination problem is formulated on the basis of CP, and a large neighborhood search–based heuristic is proposed to solve the problem. Commercial CP solvers are also used for comparison. Simulation results show that the proposed large neighborhood search–based heuristic outperforms the commercial CP solver with regard to both the solution quality and the computation time. Moreover, simulation results with respect to departure time of the last vessel, total sojourn time, and waiting time show significant improvement with earlier departure times and shorter sojourn times and waiting times.