A MIP Heuristic for Multi Port Stowage Planning

In this paper we extend the problem of determining how to stow a given set of containers of different types into the available locations of a containership, that is, the so-called Master Bay Plan Problem (MBPP), to the Multi-Port Master Bay Plan Problem (MP-MBPP). In the MP-MBPP the whole route of the ship is investigated; in particular, at each port of the route different sets of containers must be loaded for being shipped to the next ports. Differently from MBPP, in MP-MBPP at each port the sequence of two handling operations affects the effectiveness of a stowing plan: first, the import containers must be unloaded from the ship, then the export containers can be loaded. Only few papers in the recent literature deal with the MP-MBPP. Here, we propose a Mixed Integer Programming (MIP) heuristic based on an exact MIP model for the MP-MBPP very recently proposed in the literature; the main aim is the minimization of the total berthing time of the ship. Unproductive movements are included in the analysis, as well as the workload of the quay cranes used in each port visited by the ship. As a novel issue the new proposed MIP heuristic deals with actual operative handling operations; in particular, the presence of hatches is taken into account for the final stowage plans and different types of containers are included in the analysis, that is 20’ and 40’ standard containers, reefer and open top ones. The proposed MIP heuristic permits to find good stowage solutions in a short amount of time and thus to include the model into an effective tool that can help the liner planner during the whole trip of the ship for defining the stowage planning in accordance with the updated transport demands. Computational tests, executed for ships with increasing capacity up to a very large ship with a capacity of 18000 TEUs, show the efficacy of the proposed method.