A Hybrid Truck-Drone Pollution Routing Problem with Variable Truck Speeds, Time Windows and Topographical Considerations

Abstract

The integration of drones into last-mile delivery presents transformative potential for enhancing efficiency, providing a cost-effective, rapid, eco-friendly, and flexible solution for deliveries across urban and rural areas. Consequently, hybrid truck-drone systems have garnered significant attention for optimizing last-mile logistics. Despite extensive studies on drone-aided logistics systems, the environmental and operational dimensions remain underexplored. This research introduces the Truck Multi-Drone Pollution Routing Problem with speed, time window and topographical considerations (TMD-PRP-SWT) to address critical gaps in existing research. Key characteristics of this collaborative system—such as variable truck speed, delivery time windows for priority customers, and slope/elevation characteristics of delivery areas—are incorporated to better capture real-world conditions of last-mile parcel delivery. A mixed integer linear programming (MILP) model is formulated to minimize truck fuel consumption, drone energy expenditures, and driver labor costs. For efficiently solving large instances, an Adaptive Large Neighborhood Search (ALNS) algorithm is developed and validated. Extensive numerical experiments demonstrate substantial cost savings within this collaborative framework. Notably, adjustments in truck speed yield significant cost reductions when topographical characteristics are considered. These findings highlight promising research directions and implications for sustainable last-mile logistics.