Optimal fleet design in a ship routing problem

Abstract The problem of deciding an optimal fleet (the type of ships and the number of each type) in a real liner shipping problem is considered. The liner shipping problem is a multi-trip vehicle routing problem, and consists of deciding weekly routes for the selected ships. A solution method consisting of three phases is presented. In phase 1, all feasible single routes are generated for the largest ship available. Some of these routes will use only a small portion of the ship’s capacity and can be performed by smaller ships at less cost. This fact is used when calculating the cost of each route. In phase 2, the single routes generated in phase 1 are combined into multiple routes. By solving a set partitioning problem (phase 3), where the columns are the routes generated in phases 1 and 2, we find both the optimal fleet and the coherent routes for the fleet.