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Column generation based solution for bi-objective gate assignment problems

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  • Gülesin Sena Daş

    (Kırıkkale University
    De Montfort University)

  • Fatma Gzara

    (University of Waterloo)

Abstract

In this paper, we present a column generation-based algorithm for the bi-objective gate assignment problem (GAP) to generate gate schedules that minimize squared slack time at the gates while satisfying passenger expectations by minimizing their walking distance. While most of the literature focuses on heuristic or metaheuristic solutions for the bi-objective GAP, we propose flow-based and column-based models that lead to exact or near optimal solution approaches. The developed algorithm calculates a set of solutions to approximate the Pareto front. The algorithm is applied to the over-constrained GAP where gates are a limited resource and it is not possible to serve every flight using a gate. Our test cases are based on real data from an international airport and include various instances with flight-to-gate ratios between 23.9 and 34.7. Numerical results reveal that a set of solutions representing a compromise between the passenger-oriented and robustness-oriented objectives may be obtained with a tight optimality gap and within reasonable computational time even for these difficult problems.

Suggested Citation

  • Gülesin Sena Daş & Fatma Gzara, 2024. "Column generation based solution for bi-objective gate assignment problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 123-151, August.
    • Handle: RePEc:spr:mathme:v:100:y:2024:i:1:d:10.1007_s00186-024-00856-1
    DOI: 10.1007/s00186-024-00856-1
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    References listed on IDEAS

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    1. Yuan Yuan & Ping Yan & Liqiang Zhao, 2020. "Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, August.
    2. R. S. Mangoubi & Dennis F. X. Mathaisel, 1985. "Optimizing Gate Assignments at Airport Terminals," Transportation Science, INFORMS, vol. 19(2), pages 173-188, May.
    3. Daş, Gülesin Sena & Gzara, Fatma & Stützle, Thomas, 2020. "A review on airport gate assignment problems: Single versus multi objective approaches," Omega, Elsevier, vol. 92(C).
    4. Karsu, Özlem & Azizoğlu, Meral & Alanlı, Kerem, 2021. "Exact and heuristic solution approaches for the airport gate assignment problem," Omega, Elsevier, vol. 103(C).
    5. Ulrich Dorndorf & Florian Jaehn & Erwin Pesch, 2008. "Modelling Robust Flight-Gate Scheduling as a Clique Partitioning Problem," Transportation Science, INFORMS, vol. 42(3), pages 292-301, August.
    6. Cynthia Barnhart & Natashia L. Boland & Lloyd W. Clarke & Ellis L. Johnson & George L. Nemhauser & Rajesh G. Shenoi, 1998. "Flight String Models for Aircraft Fleeting and Routing," Transportation Science, INFORMS, vol. 32(3), pages 208-220, August.
    7. Şeker, Merve & Noyan, Nilay, 2012. "Stochastic optimization models for the airport gate assignment problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 438-459.
    8. Tang, Ching-Hui & Wang, Wei-Chung, 2013. "Airport gate assignments for airline-specific gates," Journal of Air Transport Management, Elsevier, vol. 30(C), pages 10-16.
    9. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    10. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.
    11. S. Ruzika & M. M. Wiecek, 2005. "Approximation Methods in Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 126(3), pages 473-501, September.
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    Cited by:

    1. Carlos Henggeler Antunes & Carlos M. Fonseca & Luís Paquete & Michael Stiglmayr, 2024. "Special issue on exact and approximation methods for mixed-integer multi-objective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 1-4, August.

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