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Complexity Results and Exact Algorithms for Robust Knapsack Problems

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Abstract

This paper studies the robust knapsack problem, for which solutions are, up to a certain point, immune from data uncertainty. We complement the works found in the literature, where uncertainty affects only the profits or only the weights of the items, by studying the complexity and approximation of the general setting with uncertainty regarding both the profits and the weights, for three different objective functions. Furthermore, we develop a scenario-relaxation algorithm for solving the general problem and present computational results.

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Notes

  1. See http://www.econ.kuleuven.be/public/ndbac96/robustKP.htm.

  2. The website http://www.econ.kuleuven.be/public/ndbac96/robustKP.htm contains the instances for n=1 000; the remaining ones can be obtained from the authors.

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Acknowledgements

The authors thank Frits Spieksma (KU Leuven) and Reviewer 1 for useful comments on an earlier version of this paper.

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Authors and Affiliations

  1. PostDoc researcher for Research Foundation—Flanders, Brussels, Belgium

    Fabrice Talla Nobibon

  2. QuantOM, HEC-Management School, University of Liège, Liège, Belgium

    Fabrice Talla Nobibon

  3. ORSTAT, Faculty of Business and Economics, KU Leuven, Leuven, Belgium

    Fabrice Talla Nobibon & Roel Leus

Authors
  1. Fabrice Talla Nobibon
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  2. Roel Leus
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Correspondence to Fabrice Talla Nobibon.

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Talla Nobibon, F., Leus, R. Complexity Results and Exact Algorithms for Robust Knapsack Problems. J Optim Theory Appl 161, 533–552 (2014). https://doi.org/10.1007/s10957-013-0319-3

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