Optimization Approaches for the Traveling Salesman Problem with Drone

The fast and cost-efficient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last mile to their customers. One technology-enabled opportunity that recently has received much attention is the use of drones to support deliveries. An innovative last-mile delivery concept in which a truck collaborates with a drone to make deliveries gives rise to a new variant of the traveling salesman problem (TSP) that we call the TSP with drone. In this paper, we model this problem as an integer program and develop several fast route-first, cluster-second heuristics based on local search and dynamic programming. We prove worst-case approximation ratios for the heuristics and test their performance by comparing the solutions to the optimal solutions for small instances. In addition, we apply our heuristics to several artificial instances with different characteristics and sizes. Our experiments show that substantial savings are possible with this concept compared to truck-only delivery.