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A Comparison of Formulations for the Single-Airport Ground-Holding Problem with Banking Constraints

Author

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  • Robert Hoffman

    (Metron Scientific Consulting, 11911 Freedom Dr. Suite 800, Reston, Virginia 20190)

  • Michael O. Ball

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

Abstract

Both the single-airport ground-holding problem (GH) and the multi-airport ground-holding problem can be extended by the addition of banking constraints to accommodate the hubbing operations of major airlines. These constraints enforce the desire of airlines to land certain groups of flights, called banks, within fixed time windows, thus preventing the propagation of delays throughout their entire operation. GH can be formulated as a transportation problem and readily solved. But in the presence of banking constraints, GH becomes a difficult integer programming problem. In this paper, we construct five different models of the single-airport ground-holding problem with banking constraints (GHB). The models are evaluated both computationally and analytically. For two of the models, we show that the banking constraints induce facets of the convex hull of the set of integer solutions. In addition, we explore a linear transformation of variables and a branching technique.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:48:y:2000:i:4:p:578-590
    DOI: 10.1287/opre.48.4.578.12417
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    References listed on IDEAS

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    1. G. Andreatta & G. Romanin-Jacur, 1987. "Aircraft Flow Management under Congestion," Transportation Science, INFORMS, vol. 21(4), pages 249-253, November.
    2. Peter B. M. Vranas & Dimitris Bertsimas & Amedeo R. Odoni, 1994. "Dynamic Ground-Holding Policies for a Network of Airports," Transportation Science, INFORMS, vol. 28(4), pages 275-291, November.
    3. 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.
    4. Mostafa Terrab & Amedeo R. Odoni, 1993. "Strategic Flow Management for Air Traffic Control," Operations Research, INFORMS, vol. 41(1), pages 138-152, February.
    5. 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.
    6. Helen Wang, 1991. "Technical Note—A Dynamic Programming Framework for the Global Flow Control Problem in Air Traffic Management," Transportation Science, INFORMS, vol. 25(4), pages 308-313, November.
    7. Octavio Richetta, 1995. "Optimal Algorithms and a Remarkably Efficient Heuristic for the Ground-Holding Problem in Air Traffic Control," Operations Research, INFORMS, vol. 43(5), pages 758-770, October.
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    Cited by:

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    2. Mukherjee, Avijit, 2004. "Dynamic Stochastic Optimization Models for Air Traffic Flow Management," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt2vk8w6nc, Institute of Transportation Studies, UC Berkeley.
    3. Wei, P. & Cao, Y. & Sun, D., 2013. "Total unimodularity and decomposition method for large-scale air traffic cell transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 53(C), pages 1-16.
    4. Dell'Olmo, Paolo & Lulli, Guglielmo, 2003. "A new hierarchical architecture for Air Traffic Management: Optimisation of airway capacity in a Free Flight scenario," European Journal of Operational Research, Elsevier, vol. 144(1), pages 179-193, January.
    5. Sun, Yanshuo & Schonfeld, Paul, 2016. "Holding decisions for correlated vehicle arrivals at intermodal freight transfer terminals," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 218-240.
    6. Thomas Vossen & Michael Ball, 2006. "Optimization and mediated bartering models for ground delay programs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(1), pages 75-90, February.
    7. Soomer, M.J. & Franx, G.J., 2008. "Scheduling aircraft landings using airlines' preferences," European Journal of Operational Research, Elsevier, vol. 190(1), pages 277-291, October.
    8. Avijit Mukherjee & Mark Hansen, 2007. "A Dynamic Stochastic Model for the Single Airport Ground Holding Problem," Transportation Science, INFORMS, vol. 41(4), pages 444-456, November.
    9. 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.
    10. Cynthia Barnhart & Dimitris Bertsimas & Constantine Caramanis & Douglas Fearing, 2012. "Equitable and Efficient Coordination in Traffic Flow Management," Transportation Science, INFORMS, vol. 46(2), pages 262-280, May.
    11. Cynthia Barnhart & Peter Belobaba & Amedeo R. Odoni, 2003. "Applications of Operations Research in the Air Transport Industry," Transportation Science, INFORMS, vol. 37(4), pages 368-391, November.
    12. Balázs Kotnyek & Octavio Richetta, 2006. "Equitable Models for the Stochastic Ground-Holding Problem Under Collaborative Decision Making," Transportation Science, INFORMS, vol. 40(2), pages 133-146, May.
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