Highlights • A new two-echelon routing problem based on heterogeneous multi-drone, named HDDP, is studied, in which a large drone carries several small drones to cooperatively realize parcel delivery. • A novel three-stage iterative optimization algorithm (IO-3S) based on the divide and conquer framework (DCF) approach is designed for solving the HDDPs. • Extensive experiments are conducted on synthetic and practical instances demonstarete the efficiency of the proposed delivery mode and IO-3S algorithm.

Abstract With the rapid development of drone technology, logistics giants like Amazon and SF Express have applied drones to parcel delivery. Drone delivery could eliminate delivery delays caused by traffic lights and traffic jams on ground vehicles, and it can deliver parcels in case of road damage caused by natural disasters. Based on this motivation, we study a new logistics delivery problem using heterogeneous multi-drone, namely, HDDP, where a large drone carries multiple small drones to distribution regions. The new features of HDDPs are multifold. First, the large drone does not directly deliver parcels, but rather launches small drones to deliver parcels. Second, the HDDP allows each small drone to deliver multiple parcels in a flight considering energy consumption according to its payload and endurance. Third, the small drone is launched from the large drone and lands at the automatic airport. In addition, we design a three-stage-based iterative optimization algorithm to reduce the complexity of the HDDP. Specifically, at the first stage, a fuzzy c-means cluster algorithm considering the small drone’s payload is designed to cluster customers; at the second stage, an improved variable neighborhood descent algorithm is developed to plan the route of the large drone; at the third stage, the dynamic programming algorithm is adopted to plan the routes of the small drones. These three stages are iteratively optimized until the termination criterion is met. Additionally, numerical experimental results indicate that the proposed algorithm for HDDP is superior to the comparison algorithms in terms of delivery time and delivery cost, and the impacts of three crucial factors are analyzed and some constructive conclusions are given.