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A Bundle Algorithm Approach for the Aircraft Schedule Recovery Problem During Hub Closures

Author

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  • Benjamin G. Thengvall

    (Graduate Program in Operations Research, Department of Mechanical Engineering, University of Texas, Austin, Texas 78712-1063)

  • Jonathan F. Bard

    (Graduate Program in Operations Research, Department of Mechanical Engineering, University of Texas, Austin, Texas 78712-1063)

  • Gang Yu

    (Department of Management Science and Information Systems, Graduate School of Business, University of Texas, Austin, Texas 78712-1175)

Abstract

A bundle algorithm is presented to solve a multicommodity network model for determining a recovery plan for a single carrier with multiple fleets following a hub closure. The algorithm is shown to provide feasible near-optimal solutions much more quickly than can be obtained using a standard commercial mixed-integer programming code (CPLEX). In this application, a bundle method is used to solve a Lagrangian relaxation of the integer programming formulation. The full algorithm includes heuristic techniques for finding feasible solutions from the solutions to the relaxed problems. Extensive computations were performed using data from Continental Airlines. The results show that the proposed approach provides faster times to optimality in some cases and always obtains feasible, near-optimal solutions for larger problems much more quickly than can be found using CPLEX. In addition, while a standard commercial code will provide only one solution, this approach provides multiple high-quality solutions.

Suggested Citation

  • Benjamin G. Thengvall & Jonathan F. Bard & Gang Yu, 2003. "A Bundle Algorithm Approach for the Aircraft Schedule Recovery Problem During Hub Closures," Transportation Science, INFORMS, vol. 37(4), pages 392-407, November.
    • Handle: RePEc:inm:ortrsc:v:37:y:2003:i:4:p:392-407
    DOI: 10.1287/trsc.37.4.392.23281
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    References listed on IDEAS

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    1. Antonio Frangioni & Giorgio Gallo, 1999. "A Bundle Type Dual-Ascent Approach to Linear Multicommodity Min-Cost Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 11(4), pages 370-393, November.
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    4. Thengvall, Benjamin G. & Yu, Gang & Bard, Jonathan F., 2001. "Multiple fleet aircraft schedule recovery following hub closures," Transportation Research Part A: Policy and Practice, Elsevier, vol. 35(4), pages 289-308, May.
    5. Yan, Shangyao & Tu, Yu-ping, 1997. "Multifleet routing and multistop flight scheduling for schedule perturbation," European Journal of Operational Research, Elsevier, vol. 103(1), pages 155-169, November.
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    Cited by:

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    2. Huang, Zhouchun & Luo, Xiaodong & Jin, Xianfei & Karichery, Sureshan, 2022. "An iterative cost-driven copy generation approach for aircraft recovery problem," European Journal of Operational Research, Elsevier, vol. 301(1), pages 334-348.
    3. Brouer, Berit D. & Dirksen, Jakob & Pisinger, David & Plum, Christian E.M. & Vaaben, Bo, 2013. "The Vessel Schedule Recovery Problem (VSRP) – A MIP model for handling disruptions in liner shipping," European Journal of Operational Research, Elsevier, vol. 224(2), pages 362-374.
    4. Ding, Yida & Wandelt, Sebastian & Wu, Guohua & Xu, Yifan & Sun, Xiaoqian, 2023. "Towards efficient airline disruption recovery with reinforcement learning," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 179(C).
    5. Sato, Keisuke & Fukumura, Naoto, 2012. "Real-time freight locomotive rescheduling and uncovered train detection during disruption," European Journal of Operational Research, Elsevier, vol. 221(3), pages 636-648.
    6. Haibo Huang & Chunyan Chen, 2016. "Climatological aspects of dense fog at Urumqi Diwopu International Airport and its impacts on flight on-time performance," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 81(2), pages 1091-1106, March.
    7. Jeffery L. Kennington & Charles D. Nicholson, 2010. "The Uncapacitated Time-Space Fixed-Charge Network Flow Problem: An Empirical Investigation of Procedures for Arc Capacity Assignment," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 326-337, May.
    8. Barry C. Smith & Ellis L. Johnson, 2006. "Robust Airline Fleet Assignment: Imposing Station Purity Using Station Decomposition," Transportation Science, INFORMS, vol. 40(4), pages 497-516, November.
    9. Nianyi Wang & Huiling Wang & Shan Pei & Boyu Zhang, 2023. "A Data-Driven Heuristic Method for Irregular Flight Recovery," Mathematics, MDPI, vol. 11(11), pages 1-22, June.
    10. Abdelghany, Khaled F. & Abdelghany, Ahmed F. & Ekollu, Goutham, 2008. "An integrated decision support tool for airlines schedule recovery during irregular operations," European Journal of Operational Research, Elsevier, vol. 185(2), pages 825-848, March.
    11. Zhao, Ai & Bard, Jonathan F. & Bickel, J. Eric, 2023. "A two-stage approach to aircraft recovery under uncertainty," Journal of Air Transport Management, Elsevier, vol. 111(C).
    12. Obrad Babić & Milica Kalić & Goran Pavković & Slavica Dožić & Mirjana Čangalović, 2010. "Heuristic approach to the airline schedule disturbances problem," Transportation Planning and Technology, Taylor & Francis Journals, vol. 33(3), pages 257-280, February.

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