## 2 Literature Review
### Research Gap  
Despite the significant advancements in optimization models for ship routing, fleet deployment, and demand acceptance, several key gaps remain in the existing literature:  
1. The lack of comprehensive frameworks for coordinating ship fleet management and surging regulatory policies: While some studies have explored fleet deployment in the context of heterogeneous fleets, few models address the origin-based cost differences arising from regulatory policies, such as surcharges on certain foreign-built ships. Regulatory impacts, such as the penalties imposed on China-built ships, are often overlooked in operational models despite their significant effects on route viability and fleet deployment decisions. [PERSON] et al. [1], [PERSON] et al. [25], and [PERSON] et al. [26] investigate fleet deployment, but they do not consider regulatory policies like U.S. surcharges on China-built ships that directly influence fleet deployment strategies and routing decisions. [PERSON] et al. [27], [PERSON] et al. [28], and [PERSON] et al. [35] explore regulatory constraints like carbon taxes or fuel efficiency but do not explicitly incorporate surcharges based on ship origin or other regulatory policies into fleet deployment and routing frameworks. In contrast, our work integrates these origin-based cost differences into the optimization framework, providing a more realistic model for ship routing and fleet deployment under such regulatory pressures. 2. The limited availability of integrated optimization models that jointly consider routing, fleet assignment, and demand acceptance decisions: A recurring issue in the literature is the treatment of routing, fleet assignment, and demand acceptance as separate or loosely coupled problems. This approach limits the ability to model the intricate trade-offs between short-term cost efficiency and long-term network viability, especially in markets affected by volatile demand and regulatory shocks. [PERSON] et al. [18], [PERSON] et al. [26], and [PERSON] et al. [28] develop MILP models for routing and scheduling under specific constraints but often treat fleet deployment and demand acceptance separately, missing the dynamic interactions between these components. [PERSON] and [PERSON] [24] review network optimization but fail to provide a unified framework that integrates fleet deployment, routing, and demand acceptance within a single optimization model. [PERSON] et al. [9], [PERSON] et al. [10], and [PERSON] et al. [30] also examine these components separately, limiting the scope of their models. Our model addresses this gap by unifying routing, fleet assignment, and demand acceptance within a single framework, enabling the consideration of trade-offs between cost, fleet utilization, regulatory constraints, and demand acceptance in an integrated manner. 3. The challenge of balancing profitability and service scale under regulatory constraints: A key challenge in liner shipping optimization is the trade-off between maximizing profitability and meeting service volume targets, particularly in light of regulatory changes such as surcharges on foreign-built ships. While multi-objective optimization has been increasingly employed in shipping optimization, few models effectively address the balance between cost efficiency and service scale, especially in the context of specific regulatory pressures. [PERSON] et al. [27], [PERSON] et al. [28], and [PERSON] et al. [9] propose multi-objective models for fleet deployment and route optimization but fail to fully address the conflict between profitability and service volume. Their models typically consider cost minimization and emission reduction without taking into account the penalties and increased costs imposed by regulatory policies. [PERSON] et al. [30], [PERSON] et al. [10], and [PERSON] et al. [32] also address demand acceptance and fleet deployment but do not fully integrate the operational impact of regulatory changes on the profitability-service scale balance. [PERSON] et al.