The European Union (EU) has recently approved the inclusion of shipping in its Emissions Trading System, aiming to foster sustainable development within the shipping industry. While this new policy represents a significant step towards reducing carbon emissions, it also poses challenges for shipping companies, particularly in terms of operation costs. To assist shipping companies in devising optimal strategies under the new policy, this study proposes new techniques to determine the optimal solutions for sailing speed and the number of ships on the route, covering both EU and non-EU areas. Additionally, we demonstrate how to adjust these optimal decisions in response to changes in charged fees, fuel prices, and weekly operational costs of ships. This research offers innovative insights into the optimal decision-making process for shipping companies under the new EU policy and serves as a valuable decision-making tool to minimize total costs.

Maritime transport serves as the backbone of international trade, accounting for more than 90% of global trade. Although maritime transport is cheaper and safer than other modes of transport, it often means long sailing distances, which often results in substantial fuel consumption and emissions. Liner shipping, a vital component of maritime transport, plays an important role in achieving sustainable maritime operations, necessitating the implementation of green liner shipping practices. Therefore, this study formulates a nonlinear integer programming model for a multi-fuel engine selection optimization problem to optimally determine ship order choice in terms of the fuel engine type, fleet deployment, fuel selection, and speed optimization, with the aim of minimizing the total weekly cost containing the weekly investment cost for ship orders and the weekly fuel cost. Given the complexity of solving nonlinear models, several linearization techniques are applied to transform the nonlinear model into a linear model that can be directly solved by Gurobi. To evaluate the performance of the linear model, 20 sets of numerical instances with, at most, seven routes are conducted. The results show that among 20 numerical instances, 16 sets of numerical instances are solved to optimality within two hours. The average gap value of the remaining four sets of numerical instances that cannot be solved to optimality within two hours is 0.51%. Additionally, sensitivity analyses are performed to examine crucial parameters, such as the weekly investment cost for ordering ships, the ship ordering budget, and the potential application of new fuel engine types, thereby exploring managerial insights. In conclusion, our findings indicate that equipping ships with low-sulfur fuel oil engines proves to be the most economical advantageous option in the selected scenarios. Furthermore, ordering ships with low-sulfur fuel, oil + methanol + liquefied natural gas engines, is beneficial when the weekly investment cost for such engines does not exceed $13,000, under the current parameter value setting.

Ship fouling has significant adverse effects on vessel performance and environmental sustainability. Therefore, this research study develops a bi-level programming model to simultaneously optimize cleaning equipment deployment by cleaning service providers in the upper level and cleaning decisions by shipping companies in the lower level. To address the interaction within the bi-level problem, the model is transformed into a single-level formulation using the big-M method. This transformation greatly simplifies the complexity of the computation and reduces computation time. Numerical experiments are conducted using real-world data to evaluate the performance of the proposed models. In addition, sensitivity analyses are performed to investigate the influence of key parameters. The results indicate that cleaning service providers primarily purchase equipment in the first year based on the demand distribution. To maximize profit, they may choose to forgo a portion of the demand. The sensitivity analysis reveals that sacrificing part of the demand can lead to an additional USD 27 million in profits compared with satisfying all demand. Moreover, increasing the cleaning price reduces both demand and equipment purchases but increases total profits. Conversely, increasing purchase costs reduces profits and the total amount of equipment purchased. When service providers can no longer generate profits, they are likely to exit the market. These findings offer valuable insights for service providers and shipping companies in the practical deployment of cleaning equipment and foul cleaning decisions, respectively.