Optimal allocation and route design for station-based drone inspection of large-scale facilities

The utilization of drones to conduct inspections on industrial electricity facilities, including large-sized wind turbines and power transmission towers, has recently received significant attention, mainly due to its potential to enhance inspection efficiency and save maintenance costs. Motivated by the advantages of drones for facility inspection, we present a novel station-based drone inspection problem (SDIP) for large-scale facilities. The objective of SDIP is to determine the locations of multiple homogeneous automatic battery swap stations (ABSSs) equipped with drones, assign facility inspection tasks to the ABSSs with operation duration constraints, and design drone inspection routes with battery capacity constraints, such that minimize the sum of fixed ABSS costs and drone travel costs. The SDIP can be regarded as a variant of the location-routing problem, which is NP-hard and difficult to solve optimally. To obtain the optimal solution of SDIP efficiently, we firstly formulate this problem into an arc based formulation and a route based formulation, and then develop a logic-based Benders decomposition (LBBD) algorithm to solve it. The SDIP is decomposed into a master problem (MP) and a set of subproblems (SPs). The MP is solved by a branch-and-cut (BC) procedure. Once a feasible integer solution is found, the linear relaxation of SPs are solved by a stabilized column generation to generate Benders cuts. If the cost of all the SPs' optimal LP solutions plus the cost of the MP's solution is less that current best cost, the SPs are exactly solved by a Branch-and-Price (BP) algorithm to generate the logic cuts. The numerical results on five scales of randomly generated instances validate the effectiveness of the LBBD algorithm. Specifically, the LBBD can solve all small- and middle-sized instances, and seven out of ten large-sized instances in 1000 s. Furthermore, we conduct a sensitivity analysis by varying the attributes of ABSSs and drones, and provide valuable managerial insights for large-scale facility inspection.