Dynamic airspace management plans and assigns airspace resources to airspace users on demand to increase airspace capacity. Although many studies of air traffic flow management (ATFM) have sought to optimally allocate air traffic to get the best use of given airspace resources, few studies have focused on how to build an efficient air traffic network or how to adjust the current network in real time. This paper presents an integer program model named the dynamic air route open-close problem (DROP). DROP has a cost-based objective function which takes into account constraints such as the shortest occupancy time of routes, which are not considered in ATFM models. The aim of DROP is to determine which routes will be opened to a certain user during a given time period. Simulation results show that DROP can facilitate utilization of air routes. DROP, a simplified version of an air traffic network constructing problem, is the first step towards realizing dynamic airspace management. The combination of ATFM and DROP can facilitate decisions toward more reasonable, efficient use of limited airspace resources.