Optimization of speed and refueling strategy for liner shipping companies considering refueling at OPL

Since fuel costs account for a large proportion of ship operating costs, it is necessary to select the optimal bunkering port. In this paper, considering the scenario of a ship refueling at the alternative ports (or outer port limit, OPL) instead of the port of call on the ship's route, a nonlinear mixed-integer model is developed to determine the refueling strategy and sailing speed. By combining the piecewise function linearization, the big-M method, etc., the proposed model is solved. Taking the actual liner route as an example, the impacts of the sailing schedule, refueling time at the OPL, the distance of the detour, and the overall fuel price level on the voyage cost of the shipping enterprise are analyzed. It is shown that when the sailing time is relatively loose, choosing to refuel at the OPL can effectively reduce the voyage cost. When the total voyage time remains unchanged, the time spent refueling at the OPL and the detour distance will increase the total voyage cost. When the total sailing time and the fuel price difference between OPL and the port of call remain unchanged, as the overall fuel price increases, the cost advantage from refueling at the OPL will decrease compared to refueling at the normal port of call. The results can provide scientific basis for liner shipping companies to choose refueling ports, determine refueling volume and optimize sailing speed.