A branch-and-price method for a ship routing and scheduling problem with cargo coupling and synchronization constraints

The purpose of this paper is to present a branch-and-price method to solve a maritime pickup and delivery problem with time windows, cargo coupling, and synchronized deliveries. This problem originates from a segment of shipping called project shipping that subsists on transporting unique and specialized cargoes. The fleet of ships is heterogeneous and considered fixed. Some sets of cargoes are coupled, meaning that either all or none of them are transported. Further, some of these coupled cargoes require synchronized deliveries, restricting the time elapsed between the first and last delivery is made. The objective is to design a route and schedule for each ship that maximizes the total profit from transporting a subset of the cargoes available. A new mathematical formulation is presented and solved using branch-and-price. The subproblem is a new variant of the elementary shortest path problem with resource constraints, and is solved by dynamic programming. Finally, the computational results show that the approach presented in this paper is significantly better than existing methods for solving this problem.