Battery Electric Vehicle Traveling Salesman Problem with Drone

The idea of deploying electric vehicles and unmanned aerial vehicles (UAVs), also known as drones, to deliver packages in logistics operations has attracted increasing attention in the past few years. In this paper, we propose an innovative problem where a battery electric vehicle (BEV) paired with drone is utilized to deliver first-aid items in a rural area. This problem is termed battery electric vehicle traveling salesman problem with drone (BEVTSPD). In BEVTSPD, the BEV and the drone perform delivery tasks coordinately while the BEV can serve as a drone hub. The BEV can also refresh its battery energy to full capacity in battery-swap stations available in the network. An arc-based mixed-integer programming model defined in a multigraph is presented for BEVTSPD. An exact branch-and-price (BP) algorithm and a Variable Neighborhood Search (VNS) heuristic are developed to solve instances with up to 25 customers in one minute. Numerical experiments show that the heuristic is much more efficient than solving the arc-based model using the ILOG CPLEX solver and BP algorithm. A real-world case study and the sensitivity analysis of different parameters are also conducted and presented. The results indicate that drone speed has a more significant effect on delivery time than the BEV's driving range.