The goal of this dissertation is to improve the ability of air traffic managers to handle uncertainty and incorporate probabilistic forecast information in ground delay programs (GDPs). In particular, we investigate ways to advance the support of decision-making under uncertainty in GDPs for a single destination airport. We explore methods to model the stochasticity in GDP operations and mechanisms that respond to conditions dynamically such that the overall system performance is optimized.; Recent developments in solving the single airport ground holding problem (SAGHP) use static or dynamic stochastic programs to manage uncertainty about how airport capacities will evolve. Both static and dynamic models involve the use of scenarios that depict different possible capacity evolutions. Dynamic models also require scenario trees featuring branch points where previously similar capacity profiles become distinct. In this dissertation, we present methodologies for generating and using scenarios and scenario trees from empirical data and examine the performance of scenario-based models in a real-world setting. We find that most U.S. airports have capacity profiles that can be classified into a small number of nominal scenarios, and for a number of airports these scenarios can be naturally combined into scenario trees. The delay costs yielded from using dynamic optimization are found to be consistently and considerably lower than that from static optimization. However, the costs incurred from applying scenario-based optimization, either static or dynamic, to these airports is considerably higher than what the "theoretical" optimization results suggest, because actual capacities vary around the nominal values assumed in the optimization, and because of uncertainty in navigating scenario trees that the idealized models ignore.; In light of the shortcomings of the scenario-based models, we develop a sequential decision model that is not limited by a small set of scenarios, which we termed as "scenario-free" model. The model is formulated as a dynamic program and the challenge lies in the computational load for solving large-scale problem instances, due to the "curse of dimensionality" of dynamic programming. We present several computational strategies to manage the complexity. We show that the computational strategies reduce the computation time significantly without much loss in optimality in several test cases. We also demonstrate the computational feasibility of the model for problems of realistic scale.; Finally, we compare the performance of the scenario-based and scenario-free models solving identical problems in a real-world setting. We show that the scenario-free model leads to lower average incurred delay cost and lower variation in incurred costs. Moreover, we find the scenario-free model yields solutions that contain more balanced distributions of ground and airborne delay. Though the magnitude of cost reduction was smaller than anticipated based on earlier results, the closeness of the expected and the incurred cost and the narrower spread of the incurred costs from using the scenario-free model make it a more informational and predictable approach.
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