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An Integer Optimization Approach to Large-Scale Air Traffic Flow Management

Author

Listed:
  • Dimitris Bertsimas

    (Sloan School of Management, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Guglielmo Lulli

    (Department of Informatics, Systems and Communication, University of Milano “Bicocca,” 20126 Milano, Italy)

  • Amedeo Odoni

    (Department of Aeronautics and Astronautics, and Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

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.

Suggested Citation

  • Dimitris Bertsimas & Guglielmo Lulli & Amedeo Odoni, 2011. "An Integer Optimization Approach to Large-Scale Air Traffic Flow Management," Operations Research, INFORMS, vol. 59(1), pages 211-227, February.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:1:p:211-227
    DOI: 10.1287/opre.1100.0899
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    References listed on IDEAS

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    1. Hanif D. Sherali & Raymond W. Staats & Antonio A. Trani, 2006. "An Airspace-Planning and Collaborative Decision-Making Model: Part II---Cost Model, Data Considerations, and Computations," Transportation Science, INFORMS, vol. 40(2), pages 147-164, May.
    2. Dimitris Bertsimas & Sarah Stock Patterson, 1998. "The Air Traffic Flow Management Problem with Enroute Capacities," Operations Research, INFORMS, vol. 46(3), pages 406-422, June.
    3. Peter B. Vranas & Dimitris J. Bertsimas & Amedeo R. Odoni, 1994. "The Multi-Airport Ground-Holding Problem in Air Traffic Control," Operations Research, INFORMS, vol. 42(2), pages 249-261, April.
    4. Guglielmo Lulli & Amedeo Odoni, 2007. "The European Air Traffic Flow Management Problem," Transportation Science, INFORMS, vol. 41(4), pages 431-443, November.
    5. Hanif D. Sherali & Raymond W. Staats & Antonio A. Trani, 2003. "An Airspace Planning and Collaborative Decision-Making Model: Part I—Probabilistic Conflicts, Workload, and Equity Considerations," Transportation Science, INFORMS, vol. 37(4), pages 434-456, November.
    6. Dimitris Bertsimas & Sarah Stock Patterson, 2000. "The Traffic Flow Management Rerouting Problem in Air Traffic Control: A Dynamic Network Flow Approach," Transportation Science, INFORMS, vol. 34(3), pages 239-255, August.
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