Route, Speed, and Bunkering Optimization for LNG-fueled Tramp Ship with Alternative Bunkering Ports

To reduce emissions, shipping companies are deploying eco-friendly ships, like those powered by LNG or methanol. Unlike traditional fuels, LNG bunkering is available at a limited number of ports. At the same time, tramp or bulk ships have fewer ports of call on their shipping lines, which may necessitate LNG-fueled ships sailing to alternative bunkering ports for refueling. The selection of bunkering ports impacts the operating costs of shipping lines due to differences in fuel prices and geographical locations. Moreover, it must factor in ship speed limits to meet loading and unloading schedules. To optimize the shipping route, speeds, and bunkering plan for LNG-fueled tramp ships, we develop an arc-based mixed-integer linear programming model with the objective of minimizing total operation costs. Subsequently, we propose a leg-based formulation based on the predetermined port call orders. Finally, case studies are conducted to demonstrate the effectiveness and efficiency of the models. Experimental results indicate that the bunkering mode with alternative bunkering ports effectively reduces total operating costs without altering the total voyage time, particularly with substantial differences in fuel prices between ports.