# A Two-Stage Optimization Model for Airport Stand Allocation and Ground Support Vehicle Scheduling
## 4 Modeling
### Multi-Type Ground Support Vehicle Scheduling Model
#### 4.3.1 Vehicle Service Process and Synergy Analysis  
* Passenger stairs: passenger stairs provide boarding and deboarding services for aircraft at remote stands, including for passengers, crew members, and cleaning staff. According to the regulations, the passenger stairs should arrive at the stand 5 min before the scheduled or estimated arrival time of the flight. The service time for the passenger stairs starts when the aircraft arrives at the stand and ends when boarding is completed. Since the service duration is relatively long and the stairs are large and difficult to maneuver, they are generally assigned to a specific apron for operations. * Ferry vehicles: the ferry vehicles are used to transport passengers between remote stands and the terminal. For arriving flights, the first ferry vehicle should arrive at the assigned stand or designated waiting area at least 5 min before the scheduled/estimated arrival time of the flight, while subsequent ferry vehicles should be in position within 2 min after the departure of the first vehicle. For departing flights, depending on the aircraft type, the first ferry vehicle for C and D category aircraft should arrive at the boarding gate or designated waiting area no later than 45 min before the scheduled/target departure time; for E category aircraft, the first ferry vehicle should arrive no later than 50 min before the scheduled/target departure time, with other ferry vehicles arriving within 2 min after the departure of the previous vehicle. Different types of aircraft require a different number of ferry vehicles; for modeling purposes, the number of ferry vehicles required is set at 1, 2, and 3 for C, D, and E category aircraft, respectively. * Fuel trucks: fuel trucks are categorized into tank trucks and pipeline trucks. Tank trucks are primarily used in medium and small airports that lack underground fuel pipelines. Pipeline trucks do not have the function of transporting and storing fuel; they are more convenient and safer and are primarily suitable for large airports with underground fuel pipelines. Fueling should occur after the jet bridge or passenger stairs have been connected and confirmed by the airline representative. The airline representative is required to provide the necessary fuel amount within 5 min of the fuel truck's arrival. Fueling is generally completed 5 min before boarding begins; this study does not consider passenger boarding during fueling or special circumstances. * Water trucks: water trucks supply drinking water to aircraft. The operation can begin once the jet bridge or passenger stairs are connected, and it must be completed no later than 15 min before the scheduled/target departure time. Water trucks have limited capacity and require resource replenishment at supply points. Since the aircraft's turnaround time is generally longer than the service time, the service window for water trucks is more flexible compared to other ground support vehicles. * Baggage belt loaders and baggage tractors: baggage tractors and belt loaders are responsible for the transportation and loading/unloading of baggage. Baggage tractors shuttle between the baggage handling center and the apron to transport baggage, while belt loaders use conveyor belts to access the elevated cargo hold, assisting staff with \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Notation**} & \multicolumn{2}{c}{**Meaning**} \\ \hline \multirow{4}{*}{variables} & \multirow{2}{*}{binary decision variable, equal to 1 if the \(n\)-th vehicle of type \(v\) sequentially serves flights \(i\) and \(j\), otherwise equal to 0.} \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \cline{2-3}  & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._loading and unloading. Together, baggage tractors and belt loaders complete the baggage handling tasks for the aircraft.