Ship routing problem with berthing time clash avoidance constraints

We consider a ship routing problem in which multiple vessels have to perform pickups and deliveries of cargoes at various locations. The loading and unloading time of cargoes at pickup and delivery locations is significant, and at each of these locations we need to assign a time slot to each vessel to perform the loading/unloading task so as to avoid time clashes. This problem is motivated by the operations of feeder vessels and company-owned cargo terminals, where the shipping company wishes to coordinate the routing and the berthing time of its vessels. We develop a heuristic algorithm for the problem using set partitioning formulation and column generation techniques. The effectiveness of the heuristic is tested via extensive computational experiments.