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This paper presents a new integer programming (IP) model for large-scale instances of the air traffic flow management (ATFM) problem. The model covers all the phases of each flight-i.e., takeoff, en route cruising, and landing-and solves for an optimal combination of flow management actions, including ground-holding, rerouting, speed control, and airborne holding on a flight-by-flight basis. A distinguishing feature of the model is that it allows for rerouting decisions. This is achieved through the imposition of sets of "local" conditions that make it possible to represent rerouting options in a compact way by only introducing some new constraints. Moreover, three classes of valid inequalities are incorporated into the model to strengthen the polyhedral structure of the underlying relaxation.Computational times are short and reasonable for practical application on problem instances of size comparable to that of the entire U.S. air traffic management system. Thus, the proposed model has the potential of serving as the main engine for the preliminary identification, on a daily basis, of promising air traffic flow management interventions on a national scale in the United States or on a continental scale in Europe.

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T his paper presents an overview of several important areas of operations research applications in the air transport industry. Specific areas covered are: the various stages of aircraft and crew schedule planning; revenue management, including overbooking and legbased and network-based seat inventory management; and the planning and operations of aviation infrastructure (airports and air traffic management). For each of these areas, the paper provides a historical perspective on OR contributions, as well as a brief summary of the state of the art. It also identifies some of the main challenges for future research.

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Consider a complete graph G = (K, E) in which each node is present with probability p,. We are interested in solving combinatorial optimization problems on subsets of nodes which are present with a certain probability. We introduce the idea of a priori optimization as a strategy competitive to the strategy of reoptimization, under which the combinatorial optimization problem is solved optimally for every instance. We consider four problems: the traveling salesman problem (TSP), the minimum spanning tree, vehicle routing, and traveling salesman facility location. We discuss the applicability of a priori optimization strategies in several areas and show that if the nodes are randomly distributed in the plane the a priori and reoptimization strategies are very close in terms of performance. We characterize the complexity of a priori optimization and address the question of approximating the optimal a priori solutions with polynomial time heuristics with provable worst-case guarantees. Finally, we use the TSP as an example to find practical solutions based on ideas of local optimality.

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