# A Two-Stage Optimization Model for Airport Stand Allocation and Ground Support Vehicle Scheduling
## 6 Numerical Study
### Results and Discussion
#### 6.2.2 Ground Support Vehicle Scheduling  
Table 8 shows a comparison of scheduling results between the FCFS strategy and LS-NSGA-II algorithms. From the table, it is evident that the LS-NSGA-II algorithm significantly improves upon the FCFS approach, particularly in optimizing waiting time and driving distance. The model improved vehicle utilization efficiency by 37.5%, reduced travel distance by 20.4%, and decreased waiting time by 57.6%. Due to the demand of flights and the number of tasks, the reduction in the number of some types of vehicles, like ferry vehicles and passenger stairs, is not significant. Notably, the number of baggage belt loaders and baggage tractors shows a significant optimization, as only about half the number of vehicles scheduled under the FCFS approach is required to meet the demand. Figures 9 and 10 compare the results of FCFS and LS-NSGA-II using examples of water trucks. In Figure 9a, since LS-NSGA-II uses fewer vehicles than FCFS, each vehicle handles more flight tasks than in FCFS, resulting in a greater distance of some water trucks. However, the total distance covered by all vehicles is less than that of FCFS, indicating a more efficient task allocation for vehicles and reducing frequent terminal trips. In Figure 9b, the reasonable allocation significantly reduces the waiting time of vehicles, with some  
Figure 8: Gantt chart of stands. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Vehicle**} & \multicolumn{2}{c}{**Vehicle Quantity**} & \multicolumn{2}{c}{**Driving Distance/m**} & \multicolumn{2}{c}{**Waiting Time/min**} \\ \cline{2-7}  & **FCFS** & **LS-NSGA-II** & **FCFS** & **LS-NSGA-II** & **FCFS** & **LS-NSGA-II** \\ \hline Ferry vehicle & 10 & 9 & 397,253.81 & 341,714.73 & 293.99186 & 79.44 \\ Passenger stair & 10 & 8 & 26,395.68 & 20,953.97 & 285.08 & 157.77 \\ Fuel truck & 12 & 8 & 138,452.78 & 87,697.23 & 852.76 & 100.32 \\ Water truck & 8 & 4 & 142,632.58 & 95,009.27 & 896.53 & 63.02 \\ Baggage belt loader & 60 & 35 & 269,744.42 & 196,246.44 & 4372.17 & 2359.20 \\ Baggage tractor & 60 & 36 & 929,055.84 & 772,663.73 & 6545.82 & 2852.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of scheduling results between the FCFS strategy and LS-NSGA-II algorithms. vehicles even achieving a waiting time of zero. Figure 10 illustrates the distribution of vehicle tasks on the apron in the FCFS and LS-NSGA-II scheduling schemes. Apron 1 and 2 are located in the center of the airport, separated from Apron 3 and 4 by one runway. Therefore, vehicles move shorter distances between Apron 1 and 2 or 3 and 4, while moving around the runway to service different aprons results in longer distances. In the FCFS scheme, most vehicles need to cross three to four aprons and frequently shuttle between both sides of the runway to enter different aprons. In contrast, in the LS-NSGA-II scheme, water trucks primarily serve the same apron continuously on one side of the runway, resulting in less distance traveled. Taking the ferry vehicles and fuel truck as examples, Figure 11 illustrates the vehicle scheduling results. In Figure 11a, \"x-arr\" indicates that the ferry vehicle arrives at the stand of flight x to take arriving passengers to the exit, while \"dep-x\" indicates that the ferry vehicle takes departing passengers from the boarding gate to the stand of flight x. From the vehicle Gantt chart and the comparison between the algorithm's optimal solution and the FCFS results, the characteristics of different vehicles executing tasks can be observed. The ferry vehicles and passenger stairs are involved in passenger services and are closely linked to the aircraft's pushback times. Consequently, the time windows for these two types of vehicles are relatively tight, and their operational flexibility is limited. Therefore, the optimization of travel distance and waiting time for the dispatch of ferry  
Figure 10: Distribution of Vehicle Tasks on the Apron using FCFS and LS-NSGA-II.