Abstract:
Objectives: Low-altitude logistics can serve as a complementary feeder mode for integrated air-ground transport, especially in cities without civil transport airports but with time-sensitive air-cargo demand. This study develops a computable optimization framework in which heterogeneous UAV fleets cooperate in route planning, feeder transport, mode selection, and trunk consolidation.
Methods: A two-level framework is proposed. At the route-planning level, the urban low-altitude environment is modeled as a weighted grid with heterogeneous environmental and operational cost attributes. A multi-preference bidirectional A* algorithm generates candidate routes under fastest, eco-friendly, and balanced preferences, providing distance, time, energy-cost, and environmental-cost parameters for scheduling. At the fleet-scheduling level, a two-stage MILP model is constructed. The first stage determines transport-mode selection, fleet allocation, sortie assignment, and preliminary trunk capacity planning, while the second stage uses transfer-point arrival events to refine trunk-flight scheduling and coordinate feeder arrivals with large-UAV trunk departures.
Results: Simulation experiments show that the route-planning module generates routes consistent with different preferences. The fastest route has a length of 21.05 km and an environmental cost of 340.44 yuan, while the eco-friendly route reduces environmental cost to 326.15 yuan with a longer distance of 23.36 km. The balanced route achieves 23.08 km, 329.59 yuan, and a computation time of 0.695 s. In the 22-task full-scale scheduling case, the unified single-stage MILP contains 46,540 variables and 111,414 constraints, whereas the two-stage MILP reduces them to 4,324 variables and 7,207 constraints. The unified model reaches the 300 s time limit with a 92.7% gap, while the two-stage framework obtains a complete feasible schedule. The proposed method completes all 22 tasks with a total cost of 25,255.70 yuan, a maximum completion time of 18.92 h, and an average waiting time of 1.00 h, outperforming fixed-schedule transfer and first-stage aggregated MILP in operational efficiency.
Conclusions: The proposed framework links spatial route generation with temporal fleet scheduling for low-altitude multimodal logistics. Its main contribution is to convert heterogeneous urban environmental costs into route-level parameters and embed them into a two-stage collaborative scheduling model. The two-stage structure does not claim theoretical superiority over a unified MILP, but provides a practical balance among solution quality, model scale, and computational tractability. Future work should incorporate real logistics OD data, payload-dependent energy consumption, dynamic weather and airspace constraints, and comparisons with road direct transport and truck-air transport.