## 1 Introduction  
Operation scheduling of apron support vehicles is an important support activity at the direct preparation stage of aircraft support. The aircraft support activities at this stage should be completed within the last 30 min before the flight time. Furthermore, the maintenance and support capability of the aircraft on the apron is related to the efficiency of the aircraft's re-deployment [1, 2]. The traditional apron support vehicle operation process is derived from the stand-alone preparation process, which is formulated by the support unit based on the daily support experience. This guarantee model can accurately guarantee each aircraft, reduce guarantee errors, and ensure guarantee quality. However, the traditional support mode often results in delayed aircraft support or long-time vacancy of the vehicle [3]; furthermore, the lack of a thorough scheduling plan causes the consequences of low support efficiency and waste of support resources [4, 5]. In this case, people are accustomed to taking the ground dispatch service of the airport as a Vehicle Routing Problem with Time Windows (VRPTW) [6, 7] by considering the utilization of the vehicle reuse rate, the minimum used vehicle or the constraints, such as parallel services to analyze the problem, and an ant colony optimization algorithm [8, 9], genetic algorithm (GA) [10, 11], greedy algorithm [12], or multi-objective optimization algorithm [13] to solve the problem of guaranteed vehicles scheduling. Solving the vehicle routing problem can guarantee the shortest driving path of the vehicle, thereby reducing the guaranteed time. However, in support tasks, facing time windows and resource constraints, consideration should be taken of how to maximize the allocation of existing resources to form the best job scheduling. Many scholars regard the airport ground scheduling service problem as a Resource-Constrained Project Scheduling Problem (RCPSP) [14; 15]. Under the premise of satisfying various constraints, the resources should be reasonably allocated and used [16; 17] to reasonably schedule the internal activities of the project [18] and finally achieve the goals of compressing time and reducing costs. The RCPSP problem is an NP-hard problem. The support capability and resource configuration of vehicles are important factors to ensure vehicles on the apron. [PERSON] et al. [19] comprehensively evaluated the support capability of support vehicles from the perspectives of availability, mission success rate, and combat readiness rate, to find out the optimal configuration principle of support resources. [PERSON] et al. [20] established a model through orthogonal experimental design and simulation and believed that the number of refueling vehicles was greater than that of oxygen-filled vehicles. [PERSON] et al. [21] and [PERSON] et al. [22] divided the support personnel into levels and realized the optimal configuration of the maximum efficiency of the support personnel by establishing a dynamic model. In terms of model establishment, [PERSON] et al. [23] established a non-linear programming model featuring a balanced equipment utilization rate by using ranking theory to solve the optimal allocation scheme of support vehicles. However, only single-aircraft support was analyzed, and it was more inappropriate to prioritize the support vehicles with short working hours under the condition of multi-aircraft support. Some scholars have suggested a two-stage method [24] and a real-time scheduling algorithm [25] based on a heuristic algorithm to solve vehicle scheduling under multi-aircraft support. [PERSON] et al. [26] innovatively constructed a ferry vehicle capacity network by using the introduced virtual aircraft and ferry depots as nodes. In addition, based on the capacity network, a mixed-integer programming model was established to minimize the number of ferry vehicles required. To determine the appropriate vehicle scheduling scheme, [PERSON] et al.