Abstract: The business model of unmanned delivery has received attention, and unmanned delivery has provided a new direction for logistics distribution. As a new mode of unmanned delivery, the joint delivery mode of trucks and robots raises some scheduling problems in its application, such as complex path planning and strict time connection requirements of trucks and robots. The traditional scheduling mode is difficult to support the operation of the system. In the joint delivery system based on multiple trucks and robots, trucks serve as mobile depots for delivery robots and goods. Trucks do not serve customers, but all customers are served by delivery robots. To study the routing problem for joint delivery system based on multiple trucks and robots, a mixed integer programming (MIP) model with the objective of minimizing total cost including the traveling cost of truck, robot, and the cost of late delivery penalty is established. The MIP model makes the complex problem mathematical, considers customer time window, truck capacity and other factors, and studies the distribution decisions among different truck groups, the robot task allocation decisions, and the distribution path planning decisions of trucks and delivery robots in the joint delivery system based on multiple trucks and robots. A variable neighborhood search (VNS) algorithm is designed to solve the model, which provides an effective tool for solving practical problems. And the effectiveness of the model and algorithm is verified by numerical experiments. The experiment results show that the difference between the results of VNS algorithm and the optimal solution is 0.98% in small-scale experiments, and the calculation time is significantly shortened. In the case of large scale, the algorithm can optimize the rules up to 30.99%. Finally, through sensitivity analysis experiments, a scientific reference is provided for logistics companies to make macro-planning decisions such as the quantity allocation of trucks and the location of trucks.

Key words: delivery robot; joint delivery system; unmanned delivery; variable neighborhood search algorithm; mixed integer programming