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Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem

Author

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  • Alexander S. Estes

    (Institute for Mathematics and Its Applications, University of Minnesota—Twin Cities, Minneapolis, Minnesota 55455;)

  • Michael O. Ball

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

Abstract

We study stochastic integer programming models for assigning delays to flights that are destined for an airport whose capacity has been impacted by poor weather or some other exogenous factor. In the existing literature, empirical evidence seemed to suggest that a proposed integer programming model had a strong formulation, but no existing theoretical results explained the observation. We apply recent results concerning the polyhedra of stochastic network flow problems to explain the strength of the existing model, and we propose a model whose size scales better with the number of flights in the problem and that preserves the strength of the existing model. Computational results are provided that demonstrate the benefits of the proposed model. Finally, we define a type of equity property that is satisfied by both models.

Suggested Citation

  • Alexander S. Estes & Michael O. Ball, 2020. "Equity and Strength in Stochastic Integer Programming Models for the Dynamic Single Airport Ground-Holding Problem," Transportation Science, INFORMS, vol. 54(4), pages 944-955, July.
    • Handle: RePEc:inm:ortrsc:v:54:y:2020:i:4:p:944-955
    DOI: 10.1287/trsc.2020.0975
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    References listed on IDEAS

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    1. Michael Z. Spivey & Warren B. Powell, 2004. "The Dynamic Assignment Problem," Transportation Science, INFORMS, vol. 38(4), pages 399-419, November.
    2. 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.
    3. Yi Liu & Mark Hansen, 2016. "Incorporating Predictability Into Cost Optimization for Ground Delay Programs," Transportation Science, INFORMS, vol. 50(1), pages 132-149, February.
    4. 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.
    5. 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.
    6. Raymond K. Cheung & Warren B. Powell, 1996. "An Algorithm for Multistage Dynamic Networks with Random Arc Capacities, with an Application to Dynamic Fleet Management," Operations Research, INFORMS, vol. 44(6), pages 951-963, December.
    7. 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.
    8. 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.
    9. Avijit Mukherjee & Mark Hansen & Shon Grabbe, 2012. "Ground delay program planning under uncertainty in airport capacity," Transportation Planning and Technology, Taylor & Francis Journals, vol. 35(6), pages 611-628, June.
    10. Liu, Pei-chen Barry & Hansen, Mark & Mukherjee, Avijit, 2008. "Scenario-based air traffic flow management: From theory to practice," Transportation Research Part B: Methodological, Elsevier, vol. 42(7-8), pages 685-702, August.
    11. William C. Jordan & Mark A. Turnquist, 1983. "A Stochastic, Dynamic Network Model for Railroad Car Distribution," Transportation Science, INFORMS, vol. 17(2), pages 123-145, May.
    12. Faramroze G. Engineer & George L. Nemhauser & Martin W. P. Savelsbergh, 2011. "Dynamic Programming-Based Column Generation on Time-Expanded Networks: Application to the Dial-a-Flight Problem," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 105-119, February.
    13. 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.
    14. Richetta, Octavio & Odoni, Amedeo R., 1994. "Dynamic solution to the ground-holding problem in air traffic control," Transportation Research Part A: Policy and Practice, Elsevier, vol. 28(3), pages 167-185, May.
    15. Gregory D. Glockner & George L. Nemhauser, 2000. "A Dynamic Network Flow Problem with Uncertain arc Capacities: Formulation and Problem Structure," Operations Research, INFORMS, vol. 48(2), pages 233-242, April.
    16. 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.
    17. Michael O. Ball & Robert Hoffman & Avijit Mukherjee, 2010. "Ground Delay Program Planning Under Uncertainty Based on the Ration-by-Distance Principle," Transportation Science, INFORMS, vol. 44(1), pages 1-14, February.
    18. 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.
    19. Linos F. Frantzeskakis & Warren B. Powell, 1990. "A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems," Transportation Science, INFORMS, vol. 24(1), pages 40-57, February.
    20. Song, Haiqing & Cheung, Raymond K. & Wang, Haiyan, 2014. "An arc-exchange decomposition method for multistage dynamic networks with random arc capacities," European Journal of Operational Research, Elsevier, vol. 233(3), pages 474-487.
    21. James C. Jones & David J. Lovell & Michael O. Ball, 2018. "Stochastic Optimization Models for Transferring Delay Along Flight Trajectories to Reduce Fuel Usage," Transportation Science, INFORMS, vol. 52(1), pages 134-149, January.
    22. Warren B. Powell & Linos F. Frantzeskakis, 1994. "Restricted Recourse Strategies for Dynamic Networks with Random Arc Capacities," Transportation Science, INFORMS, vol. 28(1), pages 3-23, February.
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    Cited by:

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    2. Bolić, Tatjana & Castelli, Lorenzo & Corolli, Luca & Scaini, Giovanni, 2021. "Flexibility in strategic flight planning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 154(C).
    3. Liu, Wenjing & Zhao, Qiuhong & Delahaye, Daniel, 2022. "Research on slot allocation for airport network in the presence of uncertainty," Journal of Air Transport Management, Elsevier, vol. 104(C).

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