The traveling salesman problem with pickups, deliveries, and draft limits

We introduce a new generalization of the traveling salesman problem with pickup and delivery, that stems from applications in maritime logistics, in which each node represents a port and has a known draft limit. Each customer has a demand, characterized by a weight, and pickups and deliveries are performed by a single ship of given weight capacity. The ship is able to visit a port only if the amount of cargo it carries is compatible with the draft limit of the port. We present an integer linear programming formulation and we show how classical valid inequalities from the literature can be adapted to the considered problem. We introduce heuristic procedures and a branch-and-cut exact algorithm. We examine, through extensive computational experiments, the impact of the various cuts and the performance of the proposed algorithms.