# Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences
## 4 Numerical Example Analysis
### Resource Allocation Quantity  
In the previous subsection, the relevant parameters of the GA were explored. The numerical experimental studies of the subsequent elements were carried out with the following parameter settings as shown in Table 5.  
In Section 2, a dynamic programming model considering the difference in the arrival time of ferries was proposed for the case where the arrival and departure times of flights are fully determined. [PERSON] et al. [10] pointed out that when a flight requires multiple ferries for service, the original service is split into services that only require one ferry by introducing virtual flights. They summarized the splitting method as an equal division of in-place time (EDPT). Finally, the problem after splitting was modeled and solved using the path planning method. Without considering the difference in the arrival time of ferries, splitting services will to some extent strengthen or weaken the demand for ferry resources. Therefore, this article proposes to use dynamic programming splitting (DPS) to solve this problem. Table 6 shows the demand for ferry resources under different splitting methods. The two splitting methods of service equivalence and EDPT are 11 ferries in static problems. The DPS method reduces the demand for ferries by 1 unit. In terms of service equivalence, the ferry sub-services of the same flight have the characteristic of consistent start and end times. Due to this feature, demand is concentrated and released. When demand is relatively concentrated at a certain moment, it forces an increase in the quantity of resource allocation. This conjecture was validated in the analysis of the results. In the EDPT, the impact of the necessary boarding time of the previous ferry on subsequent ferry services was not considered, resulting in a longer requirement for the split ferry service compared to the actual ferry service time. In contrast, the DPS is a precise description of the original problem, and theoretically, the demand for resources will be more practical. To verify whether the results have significant randomness, considering the uncertainty of flight arrival and departure, multiple experiments were conducted, and the overall results are summarized in Table 7. With the fluctuation in service arrival time, the resource variation range of service equivalence and EDPT is between 10 and 14. The method in this article shows a range between 9 and 13. From an overall perspective, the results of DPS are relatively consistent under different conditions and static problems. \begin{table}
\begin{tabular}{c c} \hline \hline
**Service Splitting Method** & **Number of Ferry Vehicles** \\ \hline Service equivalence & 11 \\ EDPT & 11 \\ DPS & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The number of ferries with different splitting methods under static problems. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Input** & **Outputound** & **Resource** & **Population** & **Iteration** & **Sample Size** \\
**Ferry Service** & **Ferry Service** & **Ceiling** & **Size** & & \\ \hline
14 & 17 & 16 & 100 & 50 & 700 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The numerical values of the parameters. In the dynamic ferry scheduling problem, the uncertainty of arrival time is an important factor affecting decision making. To describe the degree of response to uncertainty in the scheme, the confidence level \(\xi\) is introduced due to the long time required to directly solve the SAA deterministic model. This article generates a large number of samples and reflects confidence \(\xi\) through sample statistical rules. When \(\xi=0\), the constraint on the inclusion of the random variable \(\hat{t}_{j}^{0}\) now relevant is not satisfied. In contrast, when \(\xi=1\), all constraints containing random variables are required to be met.