In this dissertation we address a stochastic air traffic flow management problem. This problem arises when airspace congestion is predicted, usually because of a weather disturbance, so that the number of flights passing through a volume of airspace (flow constrained area - FCA) must be reduced. We formulate an optimization model for the assignment of dispositions to flights whose preferred flight plans passed through the FCA. For each flight, the disposition can be either to depart as scheduled but via a secondary route thereby avoiding the FCA, or to use the originally intended route but to depart with a controlled (adjusted) departure time and accompanying ground delay. We model the possibility that the capacity of the FCA may increase at some future time once the weather activity clears. The model is a two-stage stochastic program that represents the time of this capacity windfall as a random variable, and determines expected costs given a second-stage decision, conditioning on that time. We also allow the initial reroutes to vary from a conservative or pessimistic approach where all reroutes avoid the weather entirely to an optimistic or hedging strategy where some or all reroute trajectories can presume that the weather will clear by the time the FCA is reached, understanding that a drastic contingency may be necessary later if this turns out not to be true. We conduct experiments allowing a range of such trajectories and draw conclusions regarding appropriate strategies.