Constraint Programming and Local Search Heuristic: a Matheuristic Approach for Routing and Scheduling Feeder Vessels in Multi-terminal Ports

In the liner shipping business, shipping ports represent the main nodes in the maritime transportation network. These ports have a collection of terminals where container vessels can load and discharge containers. However, the logistics and planning of operations differ depending on the vessel size. Large container vessels visit a single terminal, whereas smaller container vessels, or feeder vessels, visit several terminals to transport all containers within the multiple terminals of the port. In this paper, we study the Port Scheduling Problem, the problem of scheduling the operations of feeder vessels in multi-terminal ports. The resulting problem can be identified as a version of the General Shop Scheduling Problem. We consider a Constraint Programming formulation of the problem, and we propose a matheuristic solution approach for solving large instances. The proposed matheuristic is a hybrid solution method that combines Constraint Programming with a local search heuristic. The solution approach benefits from the fast search capabilities of local search algorithms to explore the solution space using an Adaptive Large Neighbourhood Search heuristic. During the search, we further use the Constraint Programming model as an intensification technique, every time a new best-known solution is found. We conduct detailed computational experiments on the PortLib instances, showing that the incorporation of Constraint Programming within the heuristic search can result in significant benefits. The high instability in solution quality obtained by local search heuristics can be lowered by a simple combination of both methods.