# A Two-Stage Optimization Model for Airport Stand Allocation and Ground Support Vehicle Scheduling
## 2 Literature Review  
Currently, extensive research has been conducted on the stand allocation problem and ground support vehicle scheduling problem. The following section reviews the latest research on stand allocation and ground support vehicle scheduling. The stand allocation problem (SAP) involves assigning aircraft activities (arrivals, departures, and intermediate parking) to aircraft stands (parking positions) with the objective of maximizing the number of passengers/ aircraft on contact stands and minimizing the number of towns movements, while meeting a range of operational and commercial requirements [3]. This problem is closely related to the gate allocation problem (GAP). This literature review focuses on studies related to the GAP. [PERSON] [4] was one of the first scholars to introduce this problem, and since then, many researchers have conducted in-depth studies on GAP variants. The stand allocation problem becomes a complex NP-hard problem due to complex airport layouts, high numbers of flights, high flight frequency, and significant turnover rates, which cause many complex factors in airport gate assignment. In most cases, this global optimization problem is nonlinear and discrete. With the development of airports, the complexity of gate allocation grows exponentially and cannot be solved by traditional mathematical methods. Therefore, there is an urgent need for an intelligent allocation method. The main methods currently in use are expert systems [5], exact algorithms [6; 7] and heuristic algorithms [8; 9; 10; 11; 12]. Stand allocation affects three main stakeholders: airport operators, airlines, and passengers [13]. Passenger demands primarily include efficient and smooth check-in processes, short walking distances within the airport, and convenient access to airport facilities such as restaurants, shops, and entertainment options. [PERSON] and [PERSON] [14] defined a cost coefficient that considers both the walking distances between connecting flights and the transfer times between flights. [PERSON] et al. [15] aimed to minimize the number of passengers who might miss their connecting flights by calculating the product of the number of transfer passengers and the time required to travel from the arrival parking to the departure gate. For airports and airlines, congestion primarily occurs in the apron area, taxiways, and runway heads, making the optimization of these bottleneck resources a key focus in the study of stand allocation problems. When flights cannot be assigned to contact stands, passengers must use ferry vehicles to travel back and forth between the stand and the terminal, which increases waiting times and decreases passenger satisfaction, particularly during adverse weather conditions, while also raising the operational costs of airport ground support resources. A common optimization objective is to minimize the number of aircraft assigned to remote stands [16]. Improving the utilization efficiency of contact stands can also reduce ground operation costs; if the parking positions for arriving flights differs from those for departing flights, it necessitates the use of towing vehicles to move aircraft, thereby incurring additional high operational costs. [PERSON] et al. [5] proposed that the arrival and allocation of stands are distinct activities and are aimed to minimize the secondary objective function of task-towing costs. The stand allocation problem is currently managed by using pre-allocated stands based on the flight schedule for the following day. However, issues such as delays, flight cancelations, and resource shortages during actual operations can interfere with these pre-allocated results, making robustness very important for stand allocation outcomes. A common method to enhance robustness is to set buffer times between adjacent flights assigned to the same stand. The time interval between two consecutive uses of a gate is referred to as the gate's idle time or slack time [17].