IDEAS home Printed from https://ideas.repec.org/a/inm/ortrsc/v54y2020i4p897-919.html
   My bibliography  Save this article

Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

Author

Listed:
  • Ahmed Khassiba

    (École nationale de l'aviation civile (ENAC), Université de Toulouse, 31055 Toulouse Cedex 4, France; Département d'informatique et de recherche opérationnelle (DIRO), Université de Montréal, Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT), Montréal, Quebec H3T 1J4, Canada)

  • Fabian Bastin

    (Département d'informatique et de recherche opérationnelle (DIRO), Université de Montréal, Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT), Montréal, Quebec H3T 1J4, Canada)

  • Sonia Cafieri

    (École nationale de l'aviation civile (ENAC), Université de Toulouse, 31055 Toulouse Cedex 4, France;)

  • Bernard Gendron

    (Département d'informatique et de recherche opérationnelle (DIRO), Université de Montréal, Centre interuniversitaire de recherche sur les réseaux d'entreprise, la logistique et le transport (CIRRELT), Montréal, Quebec H3T 1J4, Canada)

  • Marcel Mongeau

    (École nationale de l'aviation civile (ENAC), Université de Toulouse, 31055 Toulouse Cedex 4, France;)

Abstract

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

Suggested Citation

  • Ahmed Khassiba & Fabian Bastin & Sonia Cafieri & Bernard Gendron & Marcel Mongeau, 2020. "Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management," Transportation Science, INFORMS, vol. 54(4), pages 897-919, July.
  • Handle: RePEc:inm:ortrsc:v:54:y:2020:i:4:p:897-919
    DOI: 10.1287/trsc.2020.0991
    as

    Download full text from publisher

    File URL: https://doi.org/10.1287/trsc.2020.0991
    Download Restriction: no

    File URL: https://libkey.io/10.1287/trsc.2020.0991?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Hamsa Balakrishnan & Bala G. Chandran, 2010. "Algorithms for Scheduling Runway Operations Under Constrained Position Shifting," Operations Research, INFORMS, vol. 58(6), pages 1650-1665, December.
    2. Dale McDaniel & Mike Devine, 1977. "A Modified Benders' Partitioning Algorithm for Mixed Integer Programming," Management Science, INFORMS, vol. 24(3), pages 312-319, November.
    3. Rahmaniani, Ragheb & Crainic, Teodor Gabriel & Gendreau, Michel & Rei, Walter, 2017. "The Benders decomposition algorithm: A literature review," European Journal of Operational Research, Elsevier, vol. 259(3), pages 801-817.
    4. Bruce L. Miller & Harvey M. Wagner, 1965. "Chance Constrained Programming with Joint Constraints," Operations Research, INFORMS, vol. 13(6), pages 930-945, December.
    5. Bennell, Julia A. & Mesgarpour, Mohammad & Potts, Chris N., 2017. "Dynamic scheduling of aircraft landings," European Journal of Operational Research, Elsevier, vol. 258(1), pages 315-327.
    6. J. E. Beasley & M. Krishnamoorthy & Y. M. Sharaiha & D. Abramson, 2000. "Scheduling Aircraft Landings—The Static Case," Transportation Science, INFORMS, vol. 34(2), pages 180-197, May.
    7. A. Charnes & W. W. Cooper, 1963. "Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints," Operations Research, INFORMS, vol. 11(1), pages 18-39, February.
    8. Faye, Alain, 2018. "A quadratic time algorithm for computing the optimal landing times of a fixed sequence of planes," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1148-1157.
    9. Kapolke, Manu & Fürstenau, Norbert & Heidt, Andreas & Liers, Frauke & Mittendorf, Monika & Weiß, Christian, 2016. "Pre-tactical optimization of runway utilization under uncertainty," Journal of Air Transport Management, Elsevier, vol. 56(PA), pages 48-56.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marie-Sklaerder Vié & Nicolas Zufferey & Roel Leus, 2022. "Aircraft landing planning under uncertain conditions," Journal of Scheduling, Springer, vol. 25(2), pages 203-228, April.
    2. 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.
    3. Cheramin, Meysam & Saha, Apurba Kumar & Cheng, Jianqiang & Paul, Sanjoy Kumar & Jin, Hongyue, 2021. "Resilient NdFeB magnet recycling under the impacts of COVID-19 pandemic: Stochastic programming and Benders decomposition," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 155(C).
    4. Wei Zhang & Kai Wang & Alexandre Jacquillat & Shuaian Wang, 2023. "Optimized Scenario Reduction: Solving Large-Scale Stochastic Programs with Quality Guarantees," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 886-908, July.
    5. Zhen, Lu & He, Xueting & Zhuge, Dan & Wang, Shuaian, 2024. "Primal decomposition for berth planning under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 183(C).
    6. Guglielmo Lulli & Amedeo Odoni & Bruno F. Santos, 2020. "Introduction to the Special Section: Air Transportation Systems Planning and Operations Under Uncertainty," Transportation Science, INFORMS, vol. 54(4), pages 855-857, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pohl, Maximilian & Artigues, Christian & Kolisch, Rainer, 2022. "Solving the time-discrete winter runway scheduling problem: A column generation and constraint programming approach," European Journal of Operational Research, Elsevier, vol. 299(2), pages 674-689.
    2. Pohl, Maximilian & Kolisch, Rainer & Schiffer, Maximilian, 2021. "Runway scheduling during winter operations," Omega, Elsevier, vol. 102(C).
    3. Zhang, Junfeng & Zhao, Pengli & Zhang, Yu & Dai, Ximei & Sui, Dong, 2020. "Criteria selection and multi-objective optimization of aircraft landing problem," Journal of Air Transport Management, Elsevier, vol. 82(C).
    4. Ng, K.K.H. & Lee, C.K.M. & Chan, Felix T.S. & Qin, Yichen, 2017. "Robust aircraft sequencing and scheduling problem with arrival/departure delay using the min-max regret approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 115-136.
    5. Guépet, Julien & Briant, Olivier & Gayon, Jean-Philippe & Acuna-Agost, Rodrigo, 2017. "Integration of aircraft ground movements and runway operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 104(C), pages 131-149.
    6. Bilsel, R. Ufuk & Ravindran, A., 2011. "A multiobjective chance constrained programming model for supplier selection under uncertainty," Transportation Research Part B: Methodological, Elsevier, vol. 45(8), pages 1284-1300, September.
    7. Maher, Stephen J., 2021. "Implementing the branch-and-cut approach for a general purpose Benders’ decomposition framework," European Journal of Operational Research, Elsevier, vol. 290(2), pages 479-498.
    8. Chandra, Aitichya & Choubey, Nipun & Verma, Ashish & Sooraj, K.P., 2024. "Quasi-stochastic optimization model for time-based arrival scheduling considering Standard Terminal Arrival (STAR) track time and a new delay-conflict relationship," Journal of Air Transport Management, Elsevier, vol. 115(C).
    9. O. Olesen, 2006. "Comparing and Combining Two Approaches for Chance Constrained DEA," Journal of Productivity Analysis, Springer, vol. 26(2), pages 103-119, October.
    10. Maji, Chandi Charan, 1975. "Intertemporal allocation of irrigation water in the Mayurakshi Project (India): an application of deterministic and chance-constrained linear programming," ISU General Staff Papers 197501010800006381, Iowa State University, Department of Economics.
    11. Rashed Khanjani Shiraz & Madjid Tavana & Hirofumi Fukuyama, 2021. "A joint chance-constrained data envelopment analysis model with random output data," Operational Research, Springer, vol. 21(2), pages 1255-1277, June.
    12. Kumar, Pramesh & Khani, Alireza, 2022. "Planning of integrated mobility-on-demand and urban transit networks," Transportation Research Part A: Policy and Practice, Elsevier, vol. 166(C), pages 499-521.
    13. Nathan Sudermann‐Merx & Steffen Rebennack & Christian Timpe, 2021. "Crossing Minimal Edge‐Constrained Layout Planning using Benders Decomposition," Production and Operations Management, Production and Operations Management Society, vol. 30(10), pages 3429-3447, October.
    14. N. Beheshti Asl & S. A. MirHassani, 2019. "Accelerating benders decomposition: multiple cuts via multiple solutions," Journal of Combinatorial Optimization, Springer, vol. 37(3), pages 806-826, April.
    15. Jason A. D. Atkin & Geert De Maere & Edmund K. Burke & John S. Greenwood, 2013. "Addressing the Pushback Time Allocation Problem at Heathrow Airport," Transportation Science, INFORMS, vol. 47(4), pages 584-602, November.
    16. Bordley, Robert F. & Pollock, Stephen M., 2012. "Assigning resources and targets to an organization’s activities," European Journal of Operational Research, Elsevier, vol. 220(3), pages 752-761.
    17. Chen, Shuiwang & Wu, Lingxiao & Ng, Kam K.H. & Liu, Wei & Wang, Kun, 2024. "How airports enhance the environmental sustainability of operations: A critical review from the perspective of Operations Research," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 183(C).
    18. Qiushi Chen & Lei Zhao & Jan C. Fransoo & Zhe Li, 2019. "Dual-mode inventory management under a chance credit constraint," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 41(1), pages 147-178, March.
    19. Fengmin Xu & Meihua Wang & Yu-Hong Dai & Dachuan Xu, 2018. "A sparse enhanced indexation model with chance and cardinality constraints," Journal of Global Optimization, Springer, vol. 70(1), pages 5-25, January.
    20. Robert F. Bordley & Stephen M. Pollock, 2009. "A Decision-Analytic Approach to Reliability-Based Design Optimization," Operations Research, INFORMS, vol. 57(5), pages 1262-1270, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ortrsc:v:54:y:2020:i:4:p:897-919. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.