# A Two-Stage Optimization Model for Airport Stand Allocation and Ground Support Vehicle Scheduling
## 2 Literature Review
[PERSON] and [PERSON] [18] penalized idle times that exceed a predetermined threshold, which is derived from historical flight delay statistics. [PERSON] et al. [19] employ the concept of recoverable robustness to obtain a recoverable robust solution for the gate assignment problem. It discusses and tests four objective functions to evaluate the efficiency of the gate assignment plan. The ground handling of flights involves coordinated collaboration among airports, airlines, and air traffic control, with flight arrivals and departures being dynamic and subject to time constraints. The coordination among various ground support vehicles follows a specific sequence and is subject to resource limitations. The primary task of ground handling is to assign ground support vehicles and operational time slots to aircraft within the constraints of vehicle resource limitations and standardized ground handling procedures. [PERSON] et al. [20] considered the synchronous unloading of baggage or fueling services by vehicles and workers, developing a branch-and-price heuristic method that employs traditional variable branching and innovative variable-fixing strategies. Two mathematical multi-commodity flow formulations based on spatiotemporal networks were proposed to effectively model five types of synchronization, including mobility and load synchronization. [PERSON] et al. [21] introduced a collaborative mechanism in genetic algorithms for the scheduling problem of airport baggage vehicles. [PERSON] et al. [22] formulated the scheduling problem of airport water vehicles as a vehicle routing problem (VRP), integrating the hard time windows of unmanned water vehicles servicing flights with trapezoidal fuzzy membership functions to construct flight service level functions, considering the timing rules for unmanned water vehicles servicing airport flights and further optimizing sub-paths that have not reached service capacity limits based on the C-W savings algorithm. In recent years, bionic intelligent algorithms have been extensively studied in the theoretical research of vehicle scheduling problems. These include Tabu Search algorithms [23; 24], Particle Swarm Optimization [25], Simulated Annealing [26], Ant Colony Optimization [27] and Fireworks Algorithms that mimic the natural variation patterns of fireworks [28]. These algorithms have been continuously refined and improved in terms of enhancing computational accuracy, reducing computational time, and minimizing computational space. Additionally, various algorithms have been integrated to create hybrid approaches [29], leading to many solutions tailored for increasingly complex real-world logistics problems. The aforementioned studies mainly focus on the pre-allocation phase of tasks, while research on adjusting vehicle scheduling strategies in response to changes in flight information has gradually become a hotspot in recent years. For instance, changes may occur in the arrival and departure times of service flights [30] or in the parking stands of flights [31]. Consequently, on the basis of ensuring vehicle scheduling, it is crucial to adjust vehicle routes promptly according to updated information. Such dynamic vehicle routing problems can draw on relevant studies of dynamic vehicle routing problem (DVRP) models [32; 33]. The above-mentioned literature has carried out some preliminary studies on the stand allocation problem and the optimization of ground support vehicle scheduling, and some research achievements have been made. However, it should be noted that the current research has the following shortcomings:  
1. For the stand allocation problem, the utilization of remote stands is relatively simplistic, with the focus solely on minimizing the number of flights assigned to remote stands. This approach does not fully reflect the real operational conditions of airports, and it lacks consideration of the differences between aircraft types and flight categories. 2.