Multi-objective approach for sustainable ship routing and scheduling with draft restrictions

We propose a multi-objective optimization model, which integrates different shipping operations to address the environmental sustainability and safety challenges associated with complex, practical and real-time maritime transportation problems. We formulate a mixed integer non-linear programming (MINLP) model, considering routing and scheduling of ships, time window concept regarding ports’ high tidal conditions, discrete planning horizon, loading/unloading operations, carbon emissions, and draft restrictions to maintain vessel’s safety in ports. The novelty of our research lies in (1) incorporating environmental sustainability in the optimization model by defining the relationship between fuel consumption and vessel speed to estimate the fuel consumption and carbon emissions from each vessel; (2) considering the time window to improve port’s service level by imposing penalty charges for early arrivals of vessels and for time window violation; (3) depicting the relationship between the number of containers carried by a ship with its maximum allowable draft restriction and tonnage of containerized cargo on a ship per centimetre of the draft; (4) applying two algorithms - Non-Dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) - to solve the mathematical model. Computational experiments are performed based on the practical problems of an international shipping company. Sensitivity analysis is carried out by varying the tonnage of containerized cargo loaded on the vessel per centimetre of the draft for different ports. Results associated with ship route, vessel speed, fuel consumption (tons per day), and carbon emissions rate are presented to provide an idea about the output of the mathematical model.