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Robust two-stage combinatorial optimization problems under convex second-stage cost uncertainty

Author

Listed:
  • Marc Goerigk

    (University of Siegen)

  • Adam Kasperski

    (Wrocław University of Science and Technology)

  • Paweł Zieliński

    (Wrocław University of Science and Technology)

Abstract

In this paper a class of robust two-stage combinatorial optimization problems is discussed. It is assumed that the uncertain second-stage costs are specified in the form of a convex uncertainty set, in particular polyhedral or ellipsoidal ones. It is shown that the robust two-stage versions of basic network optimization and selection problems are NP-hard, even in a very restrictive cases. Some exact and approximation algorithms for the general problem are constructed. Polynomial and approximation algorithms for the robust two-stage versions of basic problems, such as the selection and shortest path problems, are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jcomop:v:43:y:2022:i:3:d:10.1007_s10878-021-00776-4
    DOI: 10.1007/s10878-021-00776-4
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    References listed on IDEAS

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    1. Artur Alves Pessoa & Michael Poss & Ruslan Sadykov & François Vanderbeck, 2021. "Branch-Cut-and-Price for the Robust Capacitated Vehicle Routing Problem with Knapsack Uncertainty," Operations Research, INFORMS, vol. 69(3), pages 739-754, May.
    2. Yanıkoğlu, İhsan & Gorissen, Bram L. & den Hertog, Dick, 2019. "A survey of adjustable robust optimization," European Journal of Operational Research, Elsevier, vol. 277(3), pages 799-813.
    3. Marc Goerigk & Adam Kasperski & Paweł Zieliński, 2020. "Solving Robust Two-Stage Combinatorial Optimization Problems Under Convex Uncertainty," Operations Research Proceedings, in: Janis S. Neufeld & Udo Buscher & Rainer Lasch & Dominik Möst & Jörn Schönberger (ed.), Operations Research Proceedings 2019, pages 423-429, Springer.
    4. 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.
    5. 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.
    6. Dimitris Bertsimas & Melvyn Sim, 2004. "The Price of Robustness," Operations Research, INFORMS, vol. 52(1), pages 35-53, February.
    7. Amir Ardestani-Jaafari & Erick Delage, 2016. "Robust Optimization of Sums of Piecewise Linear Functions with Application to Inventory Problems," Operations Research, INFORMS, vol. 64(2), pages 474-494, April.
    8. 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.
    9. Aissi, Hassene & Bazgan, Cristina & Vanderpooten, Daniel, 2009. "Min-max and min-max regret versions of combinatorial optimization problems: A survey," European Journal of Operational Research, Elsevier, vol. 197(2), pages 427-438, September.
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