A Ship Routing Problem with Hold and Draft Constraints

Maritime transportation is an important industry, with seaborne trade estimated to be up to 85% in terms of weight of total international trade in 2007. Capital investment for ships is substantial, and the operating costs of a ship may range from thousands to tens of thousands of US dollars daily, thus the potential benefits of optimized approaches to fleet planning are significant. Despite this, there has been relatively sparse attention paid in the literature to maritime transportation in comparison to other forms of transportation such aircraft and road. We consider a single time-period ship routing problem with the following properties: a heterogeneous fleet, draft constraints, loading and discharging ports with pre-specified amounts of supply and demand, multiple material types, and capacity constrained holds in which different material types cannot be mixed. Our objective is to minimize the shipping costs while meeting the specified demands. We review a mixed integer programming model for the problem, and discuss some improvement techniques that have been implemented. We also investigate an attempt at reformulating the model, to address some inherent symmetry, using decomposition techniques: a combination of Benders Decomposition and Dantzig-Wolfe Decomposition with column generation. We find the best results for improving our original formulation are produced by a combination of methods including symmetry breaking and various types of bounding. This combination of methods performed faster than the original formulation in all attempted problem sets where it solved to completion. The performance results for the investigated decomposition reformulation are at this stage inconclusive, and some ideas for further research are suggested.