## 5 Experiments
### Basic Results
#### 5.2.2 Representative Solutions Analysis  
Based on the analysis of the Pareto frontier, three representative Pareto-optimal solutions are strategically selected for analysis in terms of route operation strategy, ship charter strategy, and route assignment, as well as transport demand assignment. These solutions, corresponding to \(k=1\), \(k=11\), and \(k=20\), were chosen to capture distinct positions along \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(k\)} & \multicolumn{2}{c}{**Obj 1**} & \multirow{2}{*}{**Obj 2**} & \multirow{2}{*}{**ORN**} & **AFR** & **TFC** & **TBC** & **The Extra** & **COIR** \\  & & & & **(USD)** & **(Million USD)** & **(Million USD)** & **Penalty Cost** & **(Million USD)** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 7: Pareto-optimal solutions of the bi-objective MIP model. the trade-off curve between maximizing Obj 1 and Obj 2. Specifically, the solution at \(k=1\) represents a strategy characterized by the highest accepted transport demand among the non-dominated set. Conversely, the solution at \(k=20\) corresponds to the highest total weekly profit. The solution at \(k=11\) serves as an intermediate point, reflecting a balanced compromise between the competing objectives. The route operation strategy of the three selected optimal solutions is detailed in Table 8.  
Table 8 shows that the 13 routes selected for operation when \(k=20\) are also part of the operational set for \(k=1\) and \(k=11\), indicating these routes are economically attractive, as the OD pairs on these routes offer higher freight rates or the ships deployed on these routes incur relatively lower transport costs. Table 9 details the ship charter and route assignment strategy for the three selected Pareto-optimal solutions. When \(k=1\), the strategy prioritizes maximizing Obj 2. This is reflected in significant charter-in activity, particularly charting in 28 20,000-TEU ships, suggesting an effort to expand the average transport capacity of available fleet. Conversely, when \(k=20\), the strategy prioritizes maximizing Obj 1. For this instance, 17 units of owned China-built 20,000-TEU ships (Type 3), 8 units of owned China-built 12,000-TEU ships (Type 1), and 7 units of owned China-built 15,000-TEU ships (Type 2) are chartered out. This indicates a smaller operational scale consistent with a profit-maximization approach. A noteworthy pattern observed across all three Pareto-optimal solutions (\(k=1\), 11, and 20) is the simultaneous chartering out of owned China-built 12,000-TEU ships (Type 1) and the chartering in of non-China-built ships of the same 12,000-TEU capacity (Type 4). For example, even at \(k=1\), while pursuing maximum volume, 4 owned Type 1 ships \begin{table}
\begin{tabular}{c c c} \hline \hline \(k\) & **ID of Object Routes** & **Total Number of Operated Routes** \\ \hline
1 & 1–17, 20 & 18 \\
11 & 1–4, 6, 8–14, 16, 17, 20 & 15 \\
20 & 1–3, 6, 8–13, 16, 17, 20 & 13 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Route operation strategy of the selected Pareto-optimal solutions. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(k\) & **The ID of Ship Types** & **ID of Assignment Routes** & **Charter in Quantity** & **Charter out Quantity** \\ \hline \multirow{5}{*}{1} & 1 & 5, 10 & 0 & 4 \\  & 2 & 7, 10, 20 & 0 & 5 \\  & 3 & 1–4, 14 & 9 & 0 \\  & 4 & 15–17 & 13 & 0 \\  & 5 & 8 & 0 & 11 \\  & 6 & 6, 8, 9, 11–13, 20 & 19 & 0 \\ \hline \multirow{5}{*}{11} & 1 & 10 & 0 & 13 \\  & 2 & 4, 10, 14 & 0 & 3 \\  & 3 & 1–3, 6, 8, 9 & 0 & 0 \\  & 4 & 16, 17 & 4 & 0 \\  & 5 & 4, 14, 20 & 0 & 0 \\  & 6 & 1, 11–14, 20 & 6 & 0 \\ \hline \multirow{5}{*}{20} & 1 & 10, 20 & 0 & 8 \\  & 2 & 1, 10, 20 & 0 & 7 \\  & 3 & 2, 3, 6, 9 & 0 & 17 \\  & 4 & 16, 17 & 4 & 0 \\  & 5 & 8, 9 & 0 & 0 \\  & 6 & 11–13 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Ship charter and route assignment strategy. are chartered out, and 13 Type 4 ships are chartered in.