On the min-cost Traveling Salesman Problem with Drone

Over the past few years, unmanned aerial vehicles (UAV), also known as drones, have been adopted as part of a new logistic method in the commercial sector called last-mile delivery. In this novel approach, they are deployed alongside trucks to deliver goods to customers to improve the quality of service and reduce the transportation cost. This approach gives rise to a new variant of the traveling salesman problem (TSP), called TSP with drone (TSP-D). A variant of this problem that aims to minimize the time at which truck and drone finish the service (or, in other words, to maximize the quality of service) was studied in the work of Murray and Chu (2015). In contrast, this paper considers a new variant of TSP-D in which the objective is to minimize operational costs including total transportation cost and one created by waste time a vehicle has to wait for the other. The problem is first formulated mathematically. Then, two algorithms are proposed for the solution. The first algorithm (TSP-LS) was adapted from the approach proposed by Murray and Chu (2015), in which an optimal TSP solution is converted to a feasible TSP-D solution by local searches. The second algorithm, a Greedy Randomized Adaptive Search Procedure (GRASP), is based on a new split procedure that optimally splits any TSP tour into a TSP-D solution. After a TSP-D solution has been generated, it is then improved through local search operators. Numerical results obtained on various instances of both objective functions with different sizes and characteristics are presented. The results show that GRASP outperforms TSP-IS in terms of solution quality under an acceptable running time.