Liner Fleet Deployment and Speed Optimization Under Emission Reduction Technologies

Maritime shipping faces stringent exhaust emission requirements because of sulfur emission regulations and the European Union Emissions Trading System (EU ETS), driving shipping companies to adopt a range of emission reduction technologies, such as scrubbers, liquefied natural gas (LNG) propulsion systems, and methanol propulsion systems. Given that many shipping companies operate fleets equipped with multiple emission reduction technologies, this study investigates an integrated fleet deployment and speed optimization problem for a shipping company operating three or more types of ships (traditional ships, scrubber-equipped ships, and LNG- or methanol-powered ships) under sulfur emission regulations and the EU ETS carbon emission regulation. A mixed-integer nonlinear programming (MINLP) model is proposed to address this optimization problem. Because of their differing regulatory mechanisms, sulfur and carbon emission regulations affect fleet deployment (i.e., the types and number of ships deployed across all routes) and speed optimization in distinct ways. As the number of ship types increases, the number of feasible fleet deployment plans grows sharply, whereas the inclusion of different ship types further complicates speed optimization, increasing the overall problem complexity. To tackle this challenge, the study performs mathematical derivations and analyses to reveal model properties and construct valid inequalities, significantly narrowing the feasible solution space. The MINLP model is first linearized according to its characteristics. Leveraging the model properties, a Benders decomposition algorithm with a tailored cut pool is developed to solve the linearized model, which serves as the foundation for a highly efficient exact algorithm for the original MINLP model. Numerical experiments show that the proposed exact algorithm achieves a nearly 90-fold reduction in computation time compared with the CPLEX-based algorithm. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72025103, 72571167, 72201163, 72394360, 72394362, 72361137001, and 72371221], the Project of Science and Technology Commission of Shanghai Municipality China [Grant 23JC1402200], and HKSAR RGC [Grant TRS T32-707/22-N]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2025.0318 .