# Ferry Scheduling Optimization Considering Arrival Time Uncertainty and In-Place Time Differences
## 4 Numerical Example Analysis
### Robustness Research  
This part mainly discusses the robustness of different scheduling schemes. Table 8 compares the robustness of scheduling schemes for static and dynamic problems. A total of 1000 simulation experiments were conducted on the scheduling schemes obtained for different scheduling problems. We calculated statistics on indicators such as average delay time and the average number of service conflicts for different scheduling schemes. In static problems, DPS is used to split services. When assuming the service arrival time remains unchanged, the required number of ferries for the scheduling plan is 10 units. The average delay duration is 68.60 min, the average number of service conflicts is 8.23, and the average transfer time between different services executed by each unit of resources is 17.38 min. This part of the time does not include the transfer time within the service. By comparison, referring to the results in Table 7, when the number of resources allocated in dynamic problems is 10, it can meet nearly 46.51% of the scenario. The number of resource allocations is also 10, but there is a significant difference in robustness between the results of static and dynamic problems. The main reason is that the configuration of 10 units of resources in the static problem is only to meet the scheduling problem in this single scenario. The 10-unit resource allocation scheme in dynamic problems is a problem that satisfies more scenarios. Therefore, whether in terms of the average number of service conflicts or the average transfer time between single resource services, the dynamic scheduling scheme exhibits good robustness. When the value of resource quantity is 9, each indicator deteriorates rapidly because in very few scenarios, the service portfolio can allow the number of resource allocations to decrease to 9. The conditions are too harsh, resulting in poor robustness of the scheme. Similarly, when the allocation of resources reaches 12 or 13, it can guarantee the majority of uncertain demand for resources. The average delay \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Service Splitting Method** & **Number of Ferry Vehicles** & **Average Delay Duration/min** & **Average Number of Service Conflicts** & **Average Transfer Time/min** \\ \hline Static scheduling & 10 & 68.60 & 8.23 & 17.38 \\  & 9 & 152.64 & 19.06 & 30.38 \\  & 10 & 26.28 & 3.08 & 9.61 \\ Dynamic scheduling & 11 & 14.26 & 1.56 & 8.97 \\  & 12 & 2.98 & 0.35 & 8.56 \\  & 13 & 0 & 0 & 8.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Robustness comparison under different resource configurations. duration and average service conflict duration of the scheduling plan are close to 0, and the average transfer time between services of the same resource is also stable at around 8.5 min. When the number of resource allocations exceeds 13, it can further reduce the transfer time, but it will lead to an increase in resource allocation costs. Figure 11 shows one of the scheduling schemes in the dynamic problem where the number of ferries required is 12. The horizontal axis represents the time axis, and the vertical axis represents the number of the ferry. The smaller the number value, the earlier the added ferry. The preceding part of the symbol \"-\" represents the flight ferry service number, while the following part represents the number of sub-services. The gray square represents the arrival time, while the black square represents the duration of the ferry service. Due to the influence of GA design, smaller numbered ferries perform more services. The newly added ferry performs fewer services. For example, resources \(r=11\) and \(r=12\) in the figure only perform one ferry service. Therefore, the load balance of the ferry still needs to be optimized. From another perspective, this scheme has good operability. The peak period of ferry entry and exit is small, and peak demand can be solved through short-term support.