# Operation Optimization of the Sea Container Fleet Based on the Double-Level Planning Model
## 3 Simulation Analysis and Verification
### Fuel Sensitivity Analysis  
Based on the ship allocation results of the route, this paper analyzes fuel sensitivity. Taking the second type of ship configured in route 1 as the research object, under the assumption that the fluctuation range of diesel and heavy oil prices is both 10%, the fuel sensitivity change is shown in Figure 3. The influence of fuel price on shipping factors is shown in Figure 4.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Scheme**} & \multirow{2}{*}{\begin{tabular}{c} **Shipping** \\ **Route** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Ship** \\ **Type** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Speed of** \\ **Ship** \\ \end{tabular} } & \multirow{2}{*}{**Quantities**} & \multirow{2}{*}{\begin{tabular}{c} **Carbon** \\ **Tav/USD** \\ **10,000** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Fuel** \\ **Cost/USD** \\ **10,000** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Airline Operating** \\ **Costs/USD** \\ **Million** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Total Operating** \\ **Costs/USD** \\ **Million** \\ \end{tabular} } \\ \hline a & 1 & 3 & 17.6 & 10 & 5.4 & 127.0 & 395.7 & \\ a & 2 & 2 & 17.7 & 11 & 5.8 & 150.1 & 493.9 & 1382.7 \\  & 3 & 1 & 18.3 & 10 & 6.6 & 155.4 & 493.1 & \\  & 1 & 3 & 17.6 & 10 & 5.4 & 127.0 & 395.7 & \\ b & 3 & 2 & 18.3 & 10 & 6.3 & 145.9 & 459.3 & 1385.7 \\  & 2 & 1 & 17.7 & 11 & 6.1 & 160.3 & 530.7 & \\ c & 2 & 3 & 17.7 & 11 & 5.5 & 141.3 & 436.5 & \\ c & 1 & 2 & 17.6 & 10 & 5.7 & 135.0 & 447.8 & 1377.4 \\  & 3 & 1 & 18.3 & 10 & 6.6 & 155.4 & 493.1 & \\  & 2 & 3 & 17.7 & 11 & 5.5 & 141.3 & 436.5 & \\ d & 3 & 2 & 18.3 & 10 & 6.3 & 145.9 & 459.3 & 1377.1 \\  & 1 & 1 & 17.6 & 10 & 6.1 & 144.1 & 481.2 & \\  & 3 & 3 & 18.3 & 10 & 6.0 & 137.5 & 406.7 & \\ e & 2 & 2 & 17.6 & 10 & 5.7 & 135.0 & 447.8 & 1385.2 \\  & 1 & 1 & 17.7 & 11 & 6.1 & 160.3 & 530.7 & \\  & 3 & 3 & 18.3 & 10 & 6.0 & 137.5 & 406.7 & \\ f & 1 & 2 & 17.7 & 11 & 5.8 & 150.1 & 493.9 & 1381.8 \\  & 2 & 1 & 17.6 & 10 & 6.1 & 144.1 & 481.2 & \\ \hline \hline \end{tabular}
\end{table}
Table 5: Allocation of route vessels.  
Figure 3: Fuel sensitivity changes.  
Figure 4a,b clearly indicate that as fuel prices rise, the optimal speed of liner shipping remains consistent, though there is a noticeable slowdown trend. Additionally, while the optimal number of ships remains stable, there is a general upward trend. Furthermore, when the optimal speed and number of ships are held constant, the fuel cost increases correspondingly with the rise in fuel prices. It is noteworthy that, at the point where the optimal speed begins to decrease while the optimal number of ships starts to rise, the increase in fuel prices actually results in a decrease in fuel costs.  
Figure 4c clearly illustrates the changes in carbon tax, total weekly operating expenses for ships, and speed under various fuel prices. As fuel prices increase, the optimal speed of liner ships remains relatively consistent within a specific range, but there is a general trend towards a gradual decrease in speed. Furthermore, the cost of carbon tax decreases gradually as the speed decreases.  
Similarly, Figure 4d shows the changes in carbon tax, the total weekly operating cost of ships, and the number of ships under different fuel prices. The optimal fleet size remains stable within a certain range, and the general trend is to increase with the rise in fuel prices. Conversely, the carbon tax cost gradually decreases. At the inflection point where the optimal fleet size increases, there is a situation where fuel prices rise while carbon tax costs decrease.