## 6 Conclusions
For example, a holistic optimization model was developed [10] that integrates sailing speed optimization with port service frequency, fleet deployment, and ship schedule design, demonstrating the benefits of joint tactical planning. Similarly, a multi-objective mixed-integer linear programming model was proposed [27] to optimize sailing speed, as well as fleet deployment and routing under carbon tax regulations, achieving cost savings of up to 15% and emission reductions of 20% on a transatlantic route. A hybrid dynamic model with receding horizon speed optimization was introduced [80], emphasizing schedule reliability and energy efficiency when port handling times are uncertain. In addition, the focus was on sailing speed optimization for near-sea shipping services, integrating container routes to improve operational efficiency [81]. With these advancements, future work can co-optimize shipping networks, fleet deployment, and sailing speeds, providing in-depth insights into how shipping companies can balance strategic and operational strategies while adapting to external policies to maintain economic and environmental sustainability. * The challenge of expanding models to accommodate multinational regulatory compliance and carbon pricing mechanisms: The current fleet deployment model can be extended to incorporate either multinational regulatory compliance or carbon pricing mechanisms to enhance its applicability in a globalized market. Dynamic fleet reallocation can further support these extensions by enabling real-time adjustments to ship assignments in response to varying regulatory requirements or carbon pricing impacts [82]. Multi-objective optimization models have been proposed to incorporate the EU Emissions Trading System (EU ETS) into China-Europe liner shipping, optimizing speed to balance emissions and costs [83]. Frameworks for carbon and cost accounting under EU ETS focus on operational adjustments like fuel choice and speed optimization to ensure compliance [84]. Bi-level programming models incorporate carbon taxes into network design, addressing route planning and fleet deployment under environmental constraints [85]. Compliance with diverse international standards, such as those for sustainable maritime operations, has also been explored to ensure operational feasibility across jurisdictions [86]. Future work could extend the current fleet deployment model to incorporate either compliance with multinational regulations, such as EU ETS and other global standards, or carbon pricing mechanisms into strategies like speed optimization, fuel choice, and route planning. These models could explore collaborative agreements or standardized practices to address regulatory variations across jurisdictions, ensuring cost-effective compliance and sustainability in a globalized market. Conceptualization, S.W. ; methodology, Y.T., Y.Y. and S.W. ; software, Y.T. ; validation, Y.T. ; formal analysis, Y.T. ; investigation, Y.T., Y.Y. and S.W. ; resources, S.W. ; data curation, Y.T. and Y.Y. ; writing--original draft preparation, Y.T., Y.Y. and S.W. ; writing--review and editing, Y.T., Y.Y. and S.W. ; visualization, Y.T. ; supervision, S.W. ; project administration, S.W. ; funding acquisition, S.W. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Institutional Review Board Statement:** Not applicable. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** The raw data supporting the conclusions of this article will be made available by the authors on request. **Conflicts of Interest:** The authors declare no conflicts of interest.