An airspace planning model for selecting flight-plans under workload, safety, and equity considerations

In this paper, we present an airspace planning model (APM) that has been developed for use in both tactical and strategic planning contexts under various airspace scenarios. Given a set of flights for a particular time horizon, along with (possibly several) alternative flight-plans for each flight that are based on delays and diversions, due to special-use airspace (SUA) restrictions prompted by launches at spaceports or adverse weather conditions, this model prescribes a set of flight-plans to be implemented. The model formulation seeks to minimize and delay fuel-cost-based objective function, subject to the constraints that each flight is assigned one of the designated flight-plans, and that the resulting set of flight-plans satisfies certain specified workload, safety, and equity criteria. These requirements ensure that the workload for air-traffic controllers in each sector is held under a permissible limit, that any potential conflicts are routinely resolvable, and that the various airlines involved derive equitable levels of benefits from the overall implemented schedule. To solve the resulting 0-1 mixed-integer programming problem more effectively using commercial software (e.g., CPLEX-MIP), we explore the use of reformulation techniques designed to more closely approximate the convex hull of feasible solutions to the problem. We also prescribe a polynomial-time heuristic procedure that is demonstrated to provide solutions to the problem within 0.01% of optimality. Computational results are reported on several scenarios based on actual flight data obtained from the Federal Aviation Administration (FAA) to demonstrate the efficacy of the proposed approach for air-traffic management (ATM) purposes.