Distributionally robust optimization of sailing speed, bunkering, and fuel switching for dual-fuel liner services

Abstract

To reduce CO₂ and SO₂ emissions, shipping companies have started deploying LNG or methanol dual-fuel ships on liner services. Unlike traditional container ships, these dual-fuel ships can use multiple types of fuels during a voyage, allowing them to comply with emission regulations while reducing operational costs through fuel switching and speed optimization. Given the significant fluctuations in bunker prices across different ports, decisions regarding fuel switching, refueling, and sailing speeds must account for price uncertainty. We develop a distributionally robust chance-constrained programming model based on the Wasserstein uncertainty set to minimize operating costs under this uncertainty. We divide each port-to-port sailing leg into sub-legs, considering regional emission requirements or canal segments. This segmentation enables the optimization of fuel usage proportions, sailing speeds, and refueling strategies for each sub-leg. The model is then reformulated as a tractable mixed-integer second-order conic programming model. We validate the model using real-world data from COSCO Shipping. Numerical experiments demonstrate that the model can identify optimal solutions for real-scale instances within practical computational time. Furthermore, the robust solutions significantly outperform those obtained using the traditional sample average approximation method. Our results suggest that the joint optimization of fuel management and sailing speeds for dual-fuel ships can effectively reduce operating costs without increasing emissions.