# A Two-Stage Optimization Model for Airport Stand Allocation and Ground Support Vehicle Scheduling
## 3 Problem Description  
A transit flight can be viewed as a pair of arriving and departing flights. When arriving, flights land sequentially on runways as directed by air traffic control, then they taxi off the runway to the assigned parking position. After reaching the parking position, the ground support service starts. Various ground support vehicles arrive at the parking area according to regulations. The turnaround process involves several stages. For contact stands, jet bridges are connected, and for remote stands, passenger stairs are used. Once passengers disembark, fueling, loading and unloading of cargo, water replenishment, wastewater disposal, and cabin cleaning services are performed. After all services are completed, passengers board, and after the boarding information is confirmed, the aircraft doors are closed. Once the turnaround services are fully completed, the flight awaits instructions from air traffic control. Depending on the stand type, the aircraft may either be towed out or taxi out on its own to the runway holding point, to prepare for departure.  
The tow tractor operates within an apron area, and it is typically responsible for 3-4 stands within that area. Since towing is the final stage of ground handling, if the departure times of flights assigned to the same tow tractor are very close, there may be a delay in towing services, leading to flight delays. Therefore, when allocating stands, the availability of tow tractors must be considered to avoid scheduling flights with similar departure times for the same tow tractor, which could cause service conflicts. Due to the large size and longer service time of passenger stairs, they are generally fixed to a specific apron area and rarely serve across different apron areas. Other ground support vehicles are not strictly limited in their operating zones. Due to the constraints of airport resources, vehicle allocation plans must be based on the stand allocation results. The distance between tasks affects the efficiency of vehicle services, excessive distance between adjacent tasks may result in flight delays due to waiting.  
Figure 2 illustrates the three working modes of ground support vehicles. The first is the continuous working mode, where ground support vehicles depart from the depot, reach the assigned parking position to service the aircraft, and then proceed to the next parking position after completing the task. Vehicles operating in a continuous working mode include towing tractors, passenger stairs, and baggage belt loaders. The second is the resource-limited working mode, where vehicles, after servicing some flights, must go to a resource supply place to replenish resources before continuing service, as they are unable to meet the demands of the next task. Vehicles in a resource-limited working mode include water trucks and catering trucks. The third is the round-trip working mode, where vehicles need to shuttle between the service place (such as terminals or baggage handling centers) and stands while providing services to the aircraft. Vehicles in a round-trip working mode include ferry vehicles and baggage tractors [34].  
A physical flight may need multiple ground support vehicles; in order to realize the one-to-one association between flight and vehicles, virtual flights are introduced.