This book provides ways for air traffic managers to better address airport capacity uncertainty in the airspace system. In particular, it discusses decision-making algorithms under uncertainty in ground delay programs (GDPs) for a single destination airport. The book proposes methods to model stochasticity in GDP operations and mechanisms to respond to conditions dynamically such that the overall system performance is optimized. The single airport ground holding problem with capacity uncertainty is modeled using two approaches: multi-stage stochastic integer programs with probabilistic capacity scenario trees and sequential decision dynamic programs with Markov capacity evolution processes. The stochastic programs require scenarios that depict capacity evolutions. Methodologies are introduced for generating and using scenario trees from empirical data. The challenge for the dynamic programs lies in the computational load for solving large-scale problems due to the curse of dimensionality. We present computational strategies to manage the complexity. In this book, we also discuss the mathematical relationship between the models and analyze their performance in a real-world setting.