A Stochastic Integer Programming Approach to Air Traffic Scheduling and Operations

Abstract

Air traffic management measures comprise tactical operating procedures to minimize delay costs and strategic scheduling interventions to control overcapacity scheduling. Although interdependent, these problems have been treated in isolation. This paper proposes an integrated model of scheduling and operations in airport networks that jointly optimizes scheduling interventions and ground-holding operations across airports networks under operating uncertainty. It is formulated as a two-stage stochastic program with integer recourse. To solve it, we develop an original decomposition algorithm with provable solution quality guarantees. The algorithm relies on new optimality cuts—dual integer cuts—that leverage the reduced costs of the dual linear programming relaxation of the second-stage problem. The algorithm also incorporates neighborhood constraints, which shift from exploration to exploitation at later stages. We also use a scenario generation approach to construct representative scenarios from historical records of operations—using integer programming. Computational experiments show that our algorithm yields near-optimal solutions for the entire U.S. National Airspace System network. Ultimately, the proposed approach enhances airport demand management models through scale integration (by capturing network-wide interdependencies) and scope integration (by capturing interdependencies between scheduling and operations).