An Optimization of the Two-Echelon Vehicle Routing Problem with Drones Considering Truck Travel Time and Carbon Emissions

Abstract

The Two-Echelon Vehicle Routing Problem with Drones (2E VRP-D) model can initiate flights from the truck, complete several deliveries to different customer locations, and then rendezvous with the truck again. In addition to economic benefits, logistics providers must consider the environmental impacts of the order-fulfillment process. A novel multi-objective optimization framework is established in this study to simultaneously minimize the total time required for truck travel while also reducing total carbon emissions. Due to restrictions in payload capacity and battery energy limits, drones need to work alongside trucks to deliver services effectively. A dynamic energy consumption model is applied for the drone, where energy use changes based on the loading rate, enabling a more realistic representation of actual operations. This complex problem is addressed using the Non-Dominated Sorting Genetic Algorithm (NSGA-II) with two approaches: the Giant Chromosome (GC) and K-means methods. Routing plans for both trucks and drones are then constructed using a novel heuristic algorithm. Overall, the K-means method delivers better average objective values, reflecting enhanced exploitation performance. Conversely, the GC method produces a higher Hypervolume (HV), indicating superior convergence and coverage of the Pareto front, supported by a lower spacing value, while K-means achieves a slightly better spread. These outcomes contribute to improving logistics operations and informing government policy decisions.