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Truck-Drone Collaborative Delivery Model Considering Potential Drone Take-off and Landing Stations
ZHONG Qingwei1, LI Yan1, YU Yingxue2, TANG Haoming1, ZHANG Yongxiang3
2026, 45(5):
63-76.
DOI: 10.3969/j.issn.1674-0696.2026.05.08
As a critical link in urban logistics, the “last mile” delivery faces challenges of low efficiency due to geographical constraints and traffic regulations that limited traditional truck-based distribution. The truck-drone collaborative delivery mode has the potential to overcome obstacles and improve timeliness; however, it imposes high requirements on drone takeoff and landing site configuration and truck-drone coordination. Considering potential drone takeoff and landing sites and comprehensive operational capabilities, a linear integer programming model that minimized total delivery time was constructed and an adaptive large neighborhood search (ALNS) algorithm incorporating a dynamic threshold acceptance criterion was proposed. Numerical experiments were conducted based on Solomon benchmark instances and real JD.com delivery cases to verify the validity of the proposed model and algorithm. The results show that: in small-scale benchmark instances, the improved ALNS can obtain a solution that is close to that of Gurobi (with an average of 415.00 seconds) within an average of 6.70 seconds, with an average Gap1 not exceeding 0.30%; in medium-scale and large-scale instances, Gurobi fails to find solutions within the prescribed time, while the improved ALNS achieves overall better delivery time than the traditional ALNS does, with a Gap2 of 9.40%. In two 100-node instances, the actual gap between the improved ALNS solution and the theoretical optimal solution does not exceed 15.20%. Compared with the truck-only mode, the collaborative delivery mode reduces delivery time by up to 19.20%, with an average saving of 13.80%. In practical examples, the collaborative delivery model can save 23.90% of the overall delivery time compared to the truck-only model. The convergence results of the algorithm indicate that the improved ALNS can accelerate convergence by dynamically adjusting the acceptance threshold. Sensitivity analysis indicates that when the drone endurance exceeds approximately 3,960 s and the payload capacity exceeds approximately 12,000 g, the improvement in delivery time diminishes significantly. In medium-scale instances, collaborative delivery efficiency is optimized when the number of potential takeoff and landing sites is approximately 7 and the spatial spacing is approximately 4,600 m. The improved ALNS based on site-feature operators reduces average delivery time by 0.40%, 1.30%, and 3.00% in small-scale, medium-scale, and large-scale instances, respectively.
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