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Bounds on the worst optimal value in interval linear programming

Soft Computing volume 23, pages 11055–11061 (2019)Cite this article

Abstract

One of the basic tools to describe uncertainty in a linear programming model is interval linear programming, where parameters are assumed to vary within a priori known intervals. One of the main topics addressed in this context is determining the optimal value range, that is, the best and the worst of all the optimal values of the objective function among all the realizations of the uncertain parameters. For the equality constraint problems, computing the best optimal value is an easy task, but the worst optimal value calculation is known to be NP-hard. In this study, we propose new methods to determine bounds for the worst optimal value, and we evaluate them on a set of randomly generated instances.

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Acknowledgements

The authors thank the two anonymous referees for their suggestions and comments which helped improve the quality and clarity of the paper.

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Authors and Affiliations

  1. Department of Industrial Engineering, University of Louisville, 132 Eastern Parkway, Louisville, KY, 40292, USA

    Mohsen Mohammadi & Monica Gentili

  2. Department of Mathematics, University of Salerno, Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy

    Monica Gentili

Authors
  1. Mohsen Mohammadi
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  2. Monica Gentili
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Correspondence to Monica Gentili.

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Mohammadi, M., Gentili, M. Bounds on the worst optimal value in interval linear programming. Soft Comput 23, 11055–11061 (2019). https://doi.org/10.1007/s00500-018-3658-z

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  • DOI: https://doi.org/10.1007/s00500-018-3658-z

Keywords

  • Interval linear programming
  • Worst optimal value
  • Bounds