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Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem

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Abstract

The current research concerns multiobjective linear programming problems with interval objective functions coefficients. It is known that the most credible solutions to these problems are necessarily efficient ones. To solve the problems, this paper attempts to propose a new model with interesting properties by considering the minimax regret criterion. The most important property of the new model is attaining a necessarily efficient solution as an optimal one whenever the set of necessarily efficient solutions is nonempty. In order to obtain an optimal solution of the new model, an algorithm is suggested. To show the performance of the proposed algorithm, numerical examples are given. Finally, some special cases are considered and their characteristic features are highlighted.

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Acknowledgments

Milan Hladík was supported by the Czech Science Foundation Grant P402-13-10660S.

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Authors and Affiliations

  1. Department of Mathematics, Yasouj University, Yasuj, Iran

    S. Rivaz

  2. Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    S. Rivaz & M. A. Yaghoobi

  3. Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Malostranské nám. 25, 11800, Prague, Czech Republic

    M. Hladík

Authors
  1. S. Rivaz
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  2. M. A. Yaghoobi
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  3. M. Hladík
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Correspondence to M. Hladík.

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Rivaz, S., Yaghoobi, M.A. & Hladík, M. Using modified maximum regret for finding a necessarily efficient solution in an interval MOLP problem. Fuzzy Optim Decis Making 15, 237–253 (2016). https://doi.org/10.1007/s10700-015-9226-4

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