IDEAS home Printed from https://ideas.repec.org/a/spr/joheur/v26y2020i4d10.1007_s10732-020-09441-1.html
   My bibliography  Save this article

Heuristic solutions to robust variants of the minimum-cost integer flow problem

Author

Listed:
  • Marko Špoljarec

    (Privredna banka Zagreb)

  • Robert Manger

    (University of Zagreb)

Abstract

This paper deals with robust optimization applied to network flows. We consider two robust variants of the minimum-cost integer flow problem. Thereby, uncertainty in problem formulation is limited to arc costs and expressed by a finite set of explicitly given scenarios. It turns out that both problem variants are NP-hard. To solve the considered variants, we propose several heuristics based on local search or evolutionary computing. We also evaluate our heuristics experimentally on appropriate problem instances.

Suggested Citation

  • Marko Špoljarec & Robert Manger, 2020. "Heuristic solutions to robust variants of the minimum-cost integer flow problem," Journal of Heuristics, Springer, vol. 26(4), pages 531-559, August.
    • Handle: RePEc:spr:joheur:v:26:y:2020:i:4:d:10.1007_s10732-020-09441-1
    DOI: 10.1007/s10732-020-09441-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10732-020-09441-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10732-020-09441-1?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
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Dimitris Bertsimas & Ebrahim Nasrabadi & Sebastian Stiller, 2013. "Robust and Adaptive Network Flows," Operations Research, INFORMS, vol. 61(5), pages 1218-1242, October.
    2. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    3. Alper Atamtürk & Muhong Zhang, 2007. "Two-Stage Robust Network Flow and Design Under Demand Uncertainty," Operations Research, INFORMS, vol. 55(4), pages 662-673, August.
    4. Roy, Bernard, 2010. "Robustness in operational research and decision aiding: A multi-faceted issue," European Journal of Operational Research, Elsevier, vol. 200(3), pages 629-638, February.
    Full references (including those not matched with items on IDEAS)

    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. Virginie Gabrel & Cécile Murat & Lei Wu, 2013. "New models for the robust shortest path problem: complexity, resolution and generalization," Annals of Operations Research, Springer, vol. 207(1), pages 97-120, August.
    2. Mengshi Lu & Zuo‐Jun Max Shen, 2021. "A Review of Robust Operations Management under Model Uncertainty," Production and Operations Management, Production and Operations Management Society, vol. 30(6), pages 1927-1943, June.
    3. Matthews, Logan R. & Gounaris, Chrysanthos E. & Kevrekidis, Ioannis G., 2019. "Designing networks with resiliency to edge failures using two-stage robust optimization," European Journal of Operational Research, Elsevier, vol. 279(3), pages 704-720.
    4. Gabrel, Virginie & Murat, Cécile & Thiele, Aurélie, 2014. "Recent advances in robust optimization: An overview," European Journal of Operational Research, Elsevier, vol. 235(3), pages 471-483.
    5. Sun, Hao & Yang, Jun & Yang, Chao, 2019. "A robust optimization approach to multi-interval location-inventory and recharging planning for electric vehicles," Omega, Elsevier, vol. 86(C), pages 59-75.
    6. Antonio G. Martín & Manuel Díaz-Madroñero & Josefa Mula, 2020. "Master production schedule using robust optimization approaches in an automobile second-tier supplier," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 143-166, March.
    7. HU, Haitao & TANG, Jiafu, 2025. "Robust facility location considering protection and backup under facility disruptions with decision-dependent uncertainty," European Journal of Operational Research, Elsevier, vol. 325(3), pages 474-486.
    8. Hassan Hijazi & Pierre Bonami & Adam Ouorou, 2013. "Robust delay-constrained routing in telecommunications," Annals of Operations Research, Springer, vol. 206(1), pages 163-181, July.
    9. Chassein, André & Goerigk, Marc & Kasperski, Adam & Zieliński, Paweł, 2018. "On recoverable and two-stage robust selection problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 265(2), pages 423-436.
    10. Filom, Siyavash & Razavi, Saiedeh, 2025. "A learning-based robust optimization framework for synchromodal freight transportation under uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 195(C).
    11. Nicolas Kämmerling & Jannis Kurtz, 2020. "Oracle-based algorithms for binary two-stage robust optimization," Computational Optimization and Applications, Springer, vol. 77(2), pages 539-569, November.
    12. Alan L. Erera & Juan C. Morales & Martin Savelsbergh, 2009. "Robust Optimization for Empty Repositioning Problems," Operations Research, INFORMS, vol. 57(2), pages 468-483, April.
    13. Catherine Cleophas & Daniel Kadatz & Sebastian Vock, 2017. "Resilient revenue management: a literature survey of recent theoretical advances," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 16(5), pages 483-498, October.
    14. Dimitris Bertsimas & Frans J. C. T. de Ruiter, 2016. "Duality in Two-Stage Adaptive Linear Optimization: Faster Computation and Stronger Bounds," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 500-511, August.
    15. Hu, Haitao & Tang, Jiafu & Tian, Tian, 2025. "Robust facility location and protection under facility disruptions with decision-dependent uncertainty," International Journal of Production Economics, Elsevier, vol. 282(C).
    16. Lebing Wang & Jian Gang Jin & Gleb Sibul & Yi Wei, 2023. "Designing Metro Network Expansion: Deterministic and Robust Optimization Models," Networks and Spatial Economics, Springer, vol. 23(1), pages 317-347, March.
    17. Christian Biefel & Martina Kuchlbauer & Frauke Liers & Lisa Waldmüller, 2025. "Robust static and dynamic maximum flows," Journal of Combinatorial Optimization, Springer, vol. 49(5), pages 1-42, July.
    18. Huang, Sen & Liu, Kanglin & Zhang, Zhi-Hai, 2023. "Column-and-constraint-generation-based approach to a robust reverse logistic network design for bike sharing," Transportation Research Part B: Methodological, Elsevier, vol. 173(C), pages 90-118.
    19. Mavrotas, George & Pechak, Olena & Siskos, Eleftherios & Doukas, Haris & Psarras, John, 2015. "Robustness analysis in Multi-Objective Mathematical Programming using Monte Carlo simulation," European Journal of Operational Research, Elsevier, vol. 240(1), pages 193-201.
    20. Oğuz Solyalı & Jean-François Cordeau & Gilbert Laporte, 2016. "The Impact of Modeling on Robust Inventory Management Under Demand Uncertainty," Management Science, INFORMS, vol. 62(4), pages 1188-1201, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:joheur:v:26:y:2020:i:4:d:10.1007_s10732-020-09441-1. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.