Resource Allocation in Flow-Constrained Areas with Stochastic Termination Times

A stochastic air traffic flow management 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 must be reduced. In the United States, in such situations, the FAA identifies the congested volume of airspace and implements an airspace flow program to regulate traffic. An optimization model was formulated for the assignment of dispositions to flights whose preferred flight plans pass through the congestion. For each flight, the disposition can be either to depart as scheduled but via a secondary route that avoids the congestion or to use the originally intended route but to depart with a controlled departure time and accompanying ground delay. The capacity of the congested area may increase 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. The goal is to minimize the expected cost over the entire distribution of possible capacity increase times.