6. Conclusion
We considered the Discrete (minimum-cost) Berth Allocation Problem (DBAP) and Hybrid (minimum-cost) Berth Allocation Problem (HBAP) with the static arrival of vessels and fixed vessel handling times. The computational experiments performed fully justify the design and further development of Sedimentation Algorithm, the exact combinatorial approach for solving DBAP and HBAP. When combined with a simple heuristic like Estimation & Rearrange Heuristic, the algorithm can be used for instances with large number of vessels as a standalone method or as a part of some more complex heuristic or meta-heuristic approach to solving DBAP or HBAP. The most difficult problems of our test instances can be solved within the time limit of 1800 s. Actually, majority of them are solved in less than 6.65 s on average, including the cases with 30 up to 60 vessels. These results indicate that this method can be used for solving real-life medium and big size instances of BAP, depending on container port layout. The differences between the minimum and maximum solving times for a large number of vessels in the test instances indicate that Sedimentation Algorithm is worth further development. We find it especially worthwhile to investigate the possibility of solving sub-problems of DBAP or HBAP that contain conflicting vessels and then combining these partial solutions to obtain the optimal solution of the entire problem. Moreover, the generalization of the algorithm to the continuous BAP and the inclusion of crane assignment to Sedimentation Algorithm are natural avenues for further development of the algorithms presented here.
