Berth allocation with time-dependent physical limitations on vessels

We consider a berth allocation problem in container terminals in which the assignment of vessels to berths is limited by water depth and tidal condition. We model the problem as a parallel-machine scheduling problem with inclusive processing set restrictions, where the time horizon is divided into two periods and the processing sets in these two periods are different. We consider both the static and dynamic cases of the problem. In the static case all of the vessels are ready for service at time zero, while in the dynamic case the vessels may have nonzero arrival times. We analyze the computational complexity and develop efficient heuristics for these two cases. Computational experiments are performed to test the effectiveness of the heuristics and to evaluate the benefits of taking tidal condition into consideration when making berth allocation decisions.