Scheduling UAV-assisted urban subway inspection services

The periodic inspection and maintenance of subway facilities are essential for ensuring system and passenger safety. However, the current manual inspection practices conducted by expert engineers are time-consuming, costly, and pose risks to workers. Unmanned aerial vehicles (UAVs) offer a promising solution for automatically inspecting subway facilities. This paper investigates an operational-level synchronized optimization problem, aiming to determine an optimal inspection timetable while simultaneously optimizing working schedules for both human teams and UAVs. Demand heterogeneity is taken into account since the variety of facilities and equipment in subway tunnels may have different required inspection cycles. By constructing “feasible and optimal task combination” sets, an Integer Linear Programming (ILP) model is formulated to address this NP-hard problem. We apply Dantzig–Wolfe decomposition to obtain a set-covering reformulation and develop an exact solution algorithm integrating Benders decomposition within a branch-and-price framework to solve the model efficiently. The approach is strengthened by implementing several tailored acceleration strategies. Extensive numerical experiments have been carried out. The results show that our proposed optimization model and algorithms can find the optimal or near-optimal solution for real-world scale instances, resulting in cost savings and improved efficiency. Furthermore, we highlight the benefits of integrated optimization by comparing our solution approach with a sequential method that addresses inspection timetables and working schedules separately.