Optimization of trucks and drones in tandem delivery network with drone trajectory planning

Drones are widely recognized as an efficient method for delivering small and lightweight parcels, such as medicines, to customers who are difficult to reach by logistic vehicles. Various studies and projects have been conducted to integrate drones into the traditional logistic service. In this approach, drones stay on trucks, take off from trucks at specific locations to make deliveries to customers, and return to the trucks to replenish and recharge. However, drone trajectories could overlap when multiple drones are used for delivery, which can lead to the risk of collisions. Consequently, the need to address the trajectory planning of drones becomes essential. This work introduces a novel truck-drone routing problem. The novelty presented by this problem lies in the integration of drone trajectory planning problems into the truck-drone routing to generate collision-free routes for drones. This concept has not been previously explored in the existing body of literature. The problem is formulated as a mixed-integer programming problem, and a matheuristic is proposed to solve it. Computational experiments show that the proposed matheuristic outperforms the commercial solver and genetic algorithm in terms of solution quality and search efficiency. Results demonstrate that the integrated truck-drone delivery mode has a lower operating cost than the mere truck mode, and including trajectory planning can prevent potential collisions.