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On a constant factor approximation for minmax regret problems using a symmetry point scenario

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  • Conde, Eduardo

Abstract

In order to find a robust solution under an unknown linear cost function it will be considered the minmax regret criterion. It is assumed the vector of costs can take on values from a given uncertainty set. The resulting optimization model has been extensively analyzed in the literature when the uncertain costs are modeled by closed intervals. Unfortunately, except for rare applications, this problem has NP-hard complexity which has led to the appearance of approximated methods seeking for good solutions in a short computational time.

Suggested Citation

  • Conde, Eduardo, 2012. "On a constant factor approximation for minmax regret problems using a symmetry point scenario," European Journal of Operational Research, Elsevier, vol. 219(2), pages 452-457.
    • Handle: RePEc:eee:ejores:v:219:y:2012:i:2:p:452-457
    DOI: 10.1016/j.ejor.2012.01.005
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    References listed on IDEAS

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    1. Conde, Eduardo, 2009. "A minmax regret approach to the critical path method with task interval times," European Journal of Operational Research, Elsevier, vol. 197(1), pages 235-242, August.
    2. Montemanni, Roberto, 2006. "A Benders decomposition approach for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1479-1490, November.
    3. Chanas, Stefan & Zielinski, Pawel, 2002. "The computational complexity of the criticality problems in a network with interval activity times," European Journal of Operational Research, Elsevier, vol. 136(3), pages 541-550, February.
    4. Averbakh, Igor & Lebedev, Vasilij, 2005. "On the complexity of minmax regret linear programming," European Journal of Operational Research, Elsevier, vol. 160(1), pages 227-231, January.
    5. Montemanni, R. & Gambardella, L. M., 2005. "A branch and bound algorithm for the robust spanning tree problem with interval data," European Journal of Operational Research, Elsevier, vol. 161(3), pages 771-779, March.
    6. Zielinski, Pawel, 2004. "The computational complexity of the relative robust shortest path problem with interval data," European Journal of Operational Research, Elsevier, vol. 158(3), pages 570-576, November.
    7. Mausser, Helmut E. & Laguna, Manuel, 1999. "A heuristic to minimax absolute regret for linear programs with interval objective function coefficients," European Journal of Operational Research, Elsevier, vol. 117(1), pages 157-174, August.
    8. Richard L. Daniels & Panagiotis Kouvelis, 1995. "Robust Scheduling to Hedge Against Processing Time Uncertainty in Single-Stage Production," Management Science, INFORMS, vol. 41(2), pages 363-376, February.
    9. Mustajoki, Jyri & Hamalainen, Raimo P. & Lindstedt, Mats R.K., 2006. "Using intervals for global sensitivity and worst-case analyses in multiattribute value trees," European Journal of Operational Research, Elsevier, vol. 174(1), pages 278-292, October.
    10. 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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    Cited by:

    1. Chassein, André B. & Goerigk, Marc, 2015. "A new bound for the midpoint solution in minmax regret optimization with an application to the robust shortest path problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 739-747.
    2. Chassein, André & Goerigk, Marc, 2017. "Minmax regret combinatorial optimization problems with ellipsoidal uncertainty sets," European Journal of Operational Research, Elsevier, vol. 258(1), pages 58-69.
    3. Fridman, Ilia & Pesch, Erwin & Shafransky, Yakov, 2020. "Minimizing maximum cost for a single machine under uncertainty of processing times," European Journal of Operational Research, Elsevier, vol. 286(2), pages 444-457.

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