Amid the swift expansion of the aviation industry, enhancing service capabilities has emerged as a critical focus for aviation companies seeking to bolster their competitive edge. Ground support services for flights are pivotal in ensuring the smooth operation of air travel. With the dynamic fluctuations in flight schedules, optimizing the allocation of airport ground service vehicles has become essential for enhancing support capabilities. This study focuses on the refueling vehicle as a case study and develops a dual-objective mixed integer programming model aimed at minimizing both the number of vehicles required and the total time spent on waiting, driving, and resource supplementation for special vehicles. An iterative algorithm, integrating the rolling time domain approach with the multi-chromosome band elite strategy from the non-dominated sorting genetic algorithm (NSGA-Ⅱ), is designed to solve the model. Experimental outcomes confirm the feasibility and efficacy of the proposed model, demonstrating its ability to effectively address special vehicle scheduling challenges within complex operational environments. This research provides a practical methodology for maximizing the utilization of airport resources.