Unmanned aerial vehicles (UAVs), increasingly vital to the success of military operations, operate in a complex and dynamic environment, sometimes in concert with manned aircraft. We present an extensible modeling framework for the solution to the dynamic resource management (DRM) problem, where airborne resources must be reassigned to time-sensitive tasks in response to changes in battlespace conditions. The DRM problem is characterized by diverse tasks with time windows, heterogeneous resources with fuel-and payload-capacity limitations, and multiple competing objectives. We propose an integer linear programing formulation for this problem, where mathematical feasibility is guaranteed. Although motivated by airborne military operations, the proposed general modeling framework is applicable to a wide array of settings, such as disaster relief operations. Additionally, land-or water-based operations may be modeled within this framework, as well as any combination of manned and unmanned vehicles.