Unmanned aerial vehicles (UAVs), as an emerging tool for data collection, are rapidly gaining popularity in monitoring patrol fields such as public security patrols, forest fire prevention, and facility inspections. To address these issues, this paper proposes a mixed-integer programming model that analogizes the allocation of monitoring resources to inventory management problems, quantifying costs due to excessive and frequent monitoring to optimize resource allocation. The model takes into account the endurance limitations of UAVs and the mechanism for splitting monitoring demands, comprehensively optimizing the allocation of inspection points, the service paths of UAVs, and the inspection cycles of each path to minimize the total operational costs of the system. To solve this model, a hybrid heuristic algorithm based on ant colony optimization (ACO) and adaptive variable neighborhood search (AVNS) is proposed. In each iteration of the algorithm, the ACO algorithm first constructes an initial solution, which is then continuously optimized in quality by the AVNS through alternate searches across six neighborhood structures. The algorithm achieves solutions comparable in quality to those of solvers in 23 small-scale instances. For a large-scale 121-node instance collected from Changsha City, the solver failes to find any feasible solution within 10 hours, while the proposed algorithm generates high-quality solutions in a short time. The effectiveness of the proposed algorithm and its excellent solution stability are validated through ablation studies.