Abstract: Based on the cluster, a new model of truck and drone joint distribution is proposed to solve the problem of difficult door-to-door delivery in rural areas. Considering the load and endurance of the drones, a mixed integer programming model with time windows is established to minimize the total operating cost, and a two-stage algorithm is proposed. First, the truck stops are calculated through the improved K-means algorithm, and then genetic simulated annealing algorithm is adopted to optimize the joint distribution route of trucks and drones. Comparing with the traditional K-means algorithm plus CPLEX results, it can prove the feasibility and effectiveness of the algorithm and model. The case study selects a rural area in Jiangsu for the application research of terminal logistics distribution. The results show that the joint delivery model of truck and drone can effectively reduce the total operating cost compared with the pure truck transportation model. The research results can provide new ideas and reference value for the application of drones in terminal distribution in rural areas.

Key words: truck and drone joint delivery, cluster, rural logistics, two-stage algorithm

摘要： 基于集群提出卡车与无人机联合配送新模式，来解决农村地区送货上门难的问题。考虑无人机载重和续航能力，以总运营成本最小为目标建立带时间窗的混合整数规划模型，并提出两阶段算法，通过改进后的K-means算法求出卡车停靠点，采用遗传模拟退火算法优化卡车与无人机联合配送路线。将其与传统K-means算法加CPLEX结果对比，可证明算法和模型的可行性与有效性。案例分析选取江苏某农村地区来进行末端物流配送的应用研究，结果表明卡车与无人机联合配送模式与纯卡车运输模式相比可有效减少总运营成本。研究成果可为农村地区末端配送中无人机的应用提供新思路和参考价值。

关键词: 卡车与无人机联合配送, 集群, 农村物流, 两阶段算法