A fleet of unmanned aerial vehicles (UAVs) supported by logistics infrastructure, such as automated service stations, may be capable of long-term persistent operations. Typically, two key stages in the deployment of such a system are resource selection and scheduling. Here, we endeavor to conduct both of these phases in concert for persistent UAV operations. We develop a mixed integer linear program (MILP) to formally describe this joint design and scheduling problem. The MILP allows UAVs to replenish their energy resources, and then return to service, using any of a number of candidate service station locations distributed throughout the field. The UAVs provide service to known deterministic customer space-time trajectories. There may be many of these customer missions occurring simultaneously in the time horizon. Each customer mission may be addressed by several UAVs. Multiple tasks may be conducted by each UAV between visits to the service stations. The MILP jointly determines the number and locations of resources (design) and their schedules to provide service to the customers. We then develop a modified receding horizon task assignment algorithm including the design problem (RHTAd) to address the computational complexity of the MILP. Numerical experiments assess the performance of RHTAd relative to the MILP solved via CPLEX. RHTA d is substantially faster with quite acceptable loss of optimality. As such, problems of much larger size can be addressed.