The importance of drone delivery services is increasing. However, the operational aspects of drone delivery services have not been studied extensively. Specifically, with respect to truck-drone systems, researchers have not given sufficient attention to drone facilities because of the limited drone flight range around a distribution center. In this paper, we propose a truck-drone system to overcome the flight-range limitation. We define a drone station as the facility where drones and charging devices are stored, usually far away from the package distribution center. The traveling salesman problem with a drone station (TSP-DS) is developed based on mixed integer programming. Fundamental features of the TSP-DS are analyzed and route distortion is defined. We show that the model can be divided into independent traveling salesman and parallel identical machine scheduling problems for which we derive two solution approaches. Computational experiments with randomly generated instances show the characteristics of the TSP-DS and suggest that our decomposition approaches effectively deal with TSP-DS complexity problems.