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A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem

Author

Listed:
  • Michael O. Ball

    (R. H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, Maryland 20742)

  • Robert Hoffman

    (Metron Aviation, Inc., 131 Elden St., Herndon, Virginia 20170)

  • Amedeo R. Odoni

    (Massachusetts Institute of Technology, Room 33-219, Cambridge, Massachusetts 02139)

  • Ryan Rifkin

    (Center for Biological and Computational Learning, 45 Carleton Street, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

In this paper, we analyze a generalization of a classic network-flow model. The generalization involves the replacement of deterministic demand with stochastic demand. While this generalization destroys the original network structure, we show that the matrix underlying the stochastic model is dual network. Thus, the integer program associated with the stochastic model can be solved efficiently using network-flow or linear-programming techniques. We also develop an application of this model to the ground-holding problem in air-traffic management. The use of this model for the ground-holding problem improves upon prior models by allowing for easy integration into the newly developed ground-delay program procedures based on the Collaborative Decision-Making paradigm.

Suggested Citation

  • Michael O. Ball & Robert Hoffman & Amedeo R. Odoni & Ryan Rifkin, 2003. "A Stochastic Integer Program with Dual Network Structure and Its Application to the Ground-Holding Problem," Operations Research, INFORMS, vol. 51(1), pages 167-171, February.
    • Handle: RePEc:inm:oropre:v:51:y:2003:i:1:p:167-171
    DOI: 10.1287/opre.51.1.167.12795
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    References listed on IDEAS

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    1. Robert E. Bixby & William H. Cunningham, 1980. "Converting Linear Programs to Network Problems," Mathematics of Operations Research, INFORMS, vol. 5(3), pages 321-357, August.
    2. Octavio Richetta & Amedeo R. Odoni, 1993. "Solving Optimally the Static Ground-Holding Policy Problem in Air Traffic Control," Transportation Science, INFORMS, vol. 27(3), pages 228-238, August.
    3. 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.
    4. 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.
    5. Robert Hoffman & Michael O. Ball, 2000. "A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints," Operations Research, INFORMS, vol. 48(4), pages 578-590, August.
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