In an effort to improve an airport operation optimization model, this research investigates the possibility of predicting probability distributions of flight delays with machine learning algorithms. The research is centered around Rotterdam The Hague Airport, a regional airport in the Netherlands. The first objective is to test how well machine learning classifiers can predict whether a flight will be delayed for a regional airport. This results in accuracies of around 70%, while taking precision and recall into account. The second objective is to predict the probability distributions of flight delays, for which three models are selected: a modified Random Forest Regressor, a Mixture Density Network and a Dropout Network. The main finding is that accurately predicting distinctive delay probability distributions for individual flights is possible. As a final objective, the predicted flight delay distributions are incorporated into an existing Flight-to-Gate Assignment Problem. It is found that this improves the robustness of the resulting schedules, although associated with a small reduction in their efficiency. The overall conclusion of this research is that machine learning-based prediction of flight delay distributions is possible, sufficiently accurate, and can improve at least one airport operation optimization problem. Further research will have to show whether this approach can be extended to other airports, other aviation optimization problems, or even optimization problems in other research areas.