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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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