Integrating drones into post-disaster logistics: a two-echelon location routing model with split deliveries and heterogeneous fleet
研究提出一个两级选址路径模型，协调地面车辆和无人机在灾后救援中的配送，通过拆分配送和异构车队优化，可将配送完成时间减少15%–42%。
The increasing frequency and severity of disasters highlight the need for responsive humanitarian logistics systems. In post-disaster settings, damaged infrastructure can delay conventional vehicle access, while drones can support timely relief delivery to locations with limited ground accessibility. This study introduces a two-echelon location-routing problem with multiple drones and split deliveries (2E-LRP-MD-SD) for coordinated ground vehicle and drone operations in post-disaster relief distribution. The problem jointly considers distribution centre selection, heterogeneous ground-vehicle deployment, multiple drones per vehicle, synchronised truck-drone routing, and split demand fulfillment. A mixed-integer linear programming formulation is developed to minimise delivery completion time while capturing accessibility asymmetry, capacity restrictions, drone endurance, and temporal synchronisation. To solve larger instances, a three-phase matheuristic, Prescriptive Analytics with Clustering and Optimisation (PACO), is proposed and benchmarked against a Variable Neighbourhood Search (VNS) metaheuristic. A modified subgradient-based lower-bound procedure supports solution-quality assessment. Computational experiments show that 2E-LRP-MD-SD reduces delivery completion time by 15%–42% relative to the ground-vehicle-only system, and that PACO consistently outperforms VNS. The sensitivity analyses show that split deliveries improve efficiency, while drone speed, fleet size, payload–endurance trade-offs, and demand intensity affect delivery completion time. The results inform configuration of truck-drone relief systems under capacity, accessibility, and demand-surge constraints.