Optimal design for an urban truck-drone collaborative delivery system enhanced with relay points

With the rapid expansion of e-commerce, the express sector has experienced significant growth, and most cities have developed comprehensive relay point (RP) infrastructures. While these facilities currently only support ground logistics, the advancement and adoption of drone technology offer the potential to enhance delivery efficiency. To address this, we propose a Relay Point-Enhanced Collaborative Truck-Drone Delivery Model (RPECTDDM) to leverage existing RP infrastructure for designing a more efficient ground-air integrated logistics system. By incorporating RPs for intermediate cargo transfers, the model optimizes: (i) RP selection, (ii) customer allocation between trucks and drones, and (iii) the routing of both trucks and drones. The problem is formulated as a mixed-integer linear programming model aimed at minimizing total costs, which include truck operations, drone deployment, and RP activation. A two-stage Adaptive Large Neighborhood Search (ALNS) algorithm is proposed to solve this computationally demanding problem. In the first stage, feasible solutions are generated using heuristic methods, while the second stage iteratively refines these solutions through destroy-and-repair operators tailored to the problem. Numerical experiments demonstrate the effectiveness of the proposed approach, achieving near-optimal solutions in reasonable computational times, even for large-scale scenarios. A real-world case study in Chengdu further highlights the advantages of the RPECTDDM, significantly reducing total costs and truck travel times compared to three benchmark models: Truck-Drone Collaborative Delivery Model (TDCDM), Relay Point Enhanced Truck Delivery Model (RPETDM), and Truck-Only Delivery Model (TODM). Specially, RPECTDDM achieves cost savings of up to 48.47 % and reduces truck travel time by 61.21 % compared to TODM. Sensitivity analyses underscore the importance of RP activation costs and drone endurance in operational planning. This study advances urban logistics by bridging the gap between theoretical models and practical implementation, offering a scalable, efficient framework for integrating trucks and drones in delivery systems.