IDEAS home Printed from https://ideas.repec.org/a/spr/mathme/v92y2020i2d10.1007_s00186-020-00712-y.html
   My bibliography  Save this article

Min max min robust (relative) regret combinatorial optimization

Author

Listed:
  • Alejandro Crema

    (Universidad Central de Venezuela)

Abstract

We consider combinatorial optimization problems with uncertainty in the cost vector. Recently, a novel approach was developed to deal with such uncertainties: instead of a single one robust solution, obtained by solving a min max problem, the authors consider a set of solutions obtained by solving a min max min problem. In this new approach, the set of solutions is computed once and we can choose the best one in real time each time a cost vector occurs yielding better solutions compared to the min max approach. In this paper, we apply the new approach to the absolute and relative regret cases. Algorithms to solve the min max min robust (relative) regret problems are presented with computational experiments.

Suggested Citation

  • Alejandro Crema, 2020. "Min max min robust (relative) regret combinatorial optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 249-283, October.
  • Handle: RePEc:spr:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00712-y
    DOI: 10.1007/s00186-020-00712-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00186-020-00712-y
    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/s00186-020-00712-y?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Adam Kasperski & Paweł Zieliński, 2016. "Robust Discrete Optimization Under Discrete and Interval Uncertainty: A Survey," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 113-143, Springer.
    2. Chassein, André & Goerigk, Marc & Kurtz, Jannis & Poss, Michael, 2019. "Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 279(2), pages 308-319.
    3. André Chassein & Marc Goerigk, 2016. "Performance Analysis in Robust Optimization," International Series in Operations Research & Management Science, in: Michael Doumpos & Constantin Zopounidis & Evangelos Grigoroudis (ed.), Robustness Analysis in Decision Aiding, Optimization, and Analytics, chapter 0, pages 145-170, Springer.
    4. Crema, Alejandro, 2000. "An algorithm for the multiparametric 0-1-integer linear programming problem relative to the objective function," European Journal of Operational Research, Elsevier, vol. 125(1), pages 18-24, August.
    5. Grani A. Hanasusanto & Daniel Kuhn & Wolfram Wiesemann, 2015. "K -Adaptability in Two-Stage Robust Binary Programming," Operations Research, INFORMS, vol. 63(4), pages 877-891, August.
    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. Alireza Amirteimoori & Simin Masrouri, 2021. "DEA-based competition strategy in the presence of undesirable products: An application to paper mills," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(2), pages 5-21.
    2. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2021. "Combinatorial two-stage minmax regret problems under interval uncertainty," Annals of Operations Research, Springer, vol. 300(1), pages 23-50, May.

    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. Ayşe N. Arslan & Boris Detienne, 2022. "Decomposition-Based Approaches for a Class of Two-Stage Robust Binary Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 857-871, March.
    2. Ayşe N. Arslan & Michael Poss & Marco Silva, 2022. "Min-Sup-Min Robust Combinatorial Optimization with Few Recourse Solutions," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2212-2228, July.
    3. Chassein, André & Goerigk, Marc, 2018. "Compromise solutions for robust combinatorial optimization with variable-sized uncertainty," European Journal of Operational Research, Elsevier, vol. 269(2), pages 544-555.
    4. Chassein, André & Goerigk, Marc & Kurtz, Jannis & Poss, Michael, 2019. "Faster algorithms for min-max-min robustness for combinatorial problems with budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 279(2), pages 308-319.
    5. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2022. "Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty," Journal of Combinatorial Optimization, Springer, vol. 43(3), pages 497-527, April.
    6. Christoph Buchheim & Jannis Kurtz, 2018. "Robust combinatorial optimization under convex and discrete cost uncertainty," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 6(3), pages 211-238, September.
    7. Cohen, Izack & Postek, Krzysztof & Shtern, Shimrit, 2023. "An adaptive robust optimization model for parallel machine scheduling," European Journal of Operational Research, Elsevier, vol. 306(1), pages 83-104.
    8. Asimit, Alexandru V. & Hu, Junlei & Xie, Yuantao, 2019. "Optimal robust insurance with a finite uncertainty set," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 67-81.
    9. Büsing, Christina & Comis, Martin & Schmidt, Eva & Streicher, Manuel, 2021. "Robust strategic planning for mobile medical units with steerable and unsteerable demands," European Journal of Operational Research, Elsevier, vol. 295(1), pages 34-50.
    10. Chassein, André & Goerigk, Marc, 2018. "Variable-sized uncertainty and inverse problems in robust optimization," European Journal of Operational Research, Elsevier, vol. 264(1), pages 17-28.
    11. Detienne, Boris & Lefebvre, Henri & Malaguti, Enrico & Monaci, Michele, 2024. "Adjustable robust optimization with objective uncertainty," European Journal of Operational Research, Elsevier, vol. 312(1), pages 373-384.
    12. Jiu, Song, 2022. "Robust omnichannel retail operations with the implementation of ship-from-store," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).
    13. Goerigk, Marc & Lendl, Stefan & Wulf, Lasse, 2022. "Recoverable robust representatives selection problems with discrete budgeted uncertainty," European Journal of Operational Research, Elsevier, vol. 303(2), pages 567-580.
    14. Feng, Wei & Feng, Yiping & Zhang, Qi, 2021. "Multistage robust mixed-integer optimization under endogenous uncertainty," European Journal of Operational Research, Elsevier, vol. 294(2), pages 460-475.
    15. Aakil M. Caunhye & Nazli Yonca Aydin & H. Sebnem Duzgun, 2020. "Robust post-disaster route restoration," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(4), pages 1055-1087, December.
    16. Omar El Housni & Vineet Goyal, 2021. "On the Optimality of Affine Policies for Budgeted Uncertainty Sets," Mathematics of Operations Research, INFORMS, vol. 46(2), pages 674-711, May.
    17. Rahal, Said & Papageorgiou, Dimitri J. & Li, Zukui, 2021. "Hybrid strategies using linear and piecewise-linear decision rules for multistage adaptive linear optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1014-1030.
    18. Buchheim, Christoph & Pruente, Jonas, 2019. "K-adaptability in stochastic combinatorial optimization under objective uncertainty," European Journal of Operational Research, Elsevier, vol. 277(3), pages 953-963.
    19. Portoleau, Tom & Artigues, Christian & Guillaume, Romain, 2024. "Robust decision trees for the multi-mode project scheduling problem with a resource investment objective and uncertain activity duration," European Journal of Operational Research, Elsevier, vol. 312(2), pages 525-540.
    20. Amadeu A. Coco & Andréa Cynthia Santos & Thiago F. Noronha, 2022. "Robust min-max regret covering problems," Computational Optimization and Applications, Springer, vol. 83(1), pages 111-141, September.

    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:mathme:v:92:y:2020:i:2:d:10.1007_s00186-020-00712-y. 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.