Optimal algorithms and a remarkably efficient heuristic for the ground-holding problem in air traffic control

Since it is safer and less expensive to absorb delays on the ground, air traffic control management tries to limit the duration of airborne delays by holding aircraft previous to departure when congestion at the airport of destination is anticipated. The problem of assigning appropriate ground-holds to aircraft is known as the ground-holding problem. Ground-holding decisions must be implemented in real time and for multiple airports; therefore, the speed of solution for algorithms is critical. This paper tests static and dynamic optimal solutions, and a very fast heuristic for the assignment of ground-holds in air traffic control. The optimal solutions are based on stochastic linear programming. The heuristic incorporates elements of stochastic modeling by utilizing information conveyed by a probabilistic forecast of airport landing capacity, while taking into consideration the dynamic nature of the problem. In extensive computational experiments based on data for Logan airport, the heuristic performed significantly better than the optimal static solution, a deterministic solution, and the passive strategy of no-ground-holds; and within 5% of the optimal dynamic solution at a fraction of the computational time. Due to its remarkable efficiency, the stochastic–dynamic heuristic appears to be a promising building block in the development of fast ground-holding algorithms for the complete network of airports.