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Outcome Range Problem in Interval Linear Programming: An Exact Approach

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Integrated Uncertainty in Knowledge Modelling and Decision Making (IUKM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 12482))

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Abstract

Interval programming provides a mathematical model for uncertain optimization problems, in which the input data can be perturbed independently within the given lower and upper bounds. This paper discusses the recently proposed outcome range problem in the context of interval linear programming. The motivation for the outcome range problem is to assess further impacts and consequences of optimal decision making, modeled in the program by an additional linear outcome function. Specifically, the goal is to compute a lower and an upper bound on the value of the given outcome function over the optimal solution set of the interval program. In this paper, we focus mainly on programs with interval coefficients in the objective function and the right-hand-side vector. For this special class of interval programs, we design an algorithm for computing the outcome range exactly, based on complementary slackness and guided basis enumeration. Finally, we perform a series of computational experiments to evaluate the performance of the proposed method.

E. Garajová and M. Rada were supported by the Czech Science Foundation under Grant P403-20-17529S. M. Hladík was supported by the Czech Science Foundation under Grant P403-18-04735S. E. Garajová and M. Hladík were also supported by the Charles University project GA UK No. 180420.

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Acknowledgements

The authors would like to thank M. Mohammadi and M. Gentili for providing the test instances and results of the fmincon method.

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Authors and Affiliations

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

    Elif Garajová & Milan Hladík

  2. Department of Econometrics, University of Economics, nám. W. Churchilla 4, Prague, Czech Republic

    Elif Garajová, Miroslav Rada & Milan Hladík

  3. Department of Financial Accounting and Auditing, University of Economics, nám. W. Churchilla 4, Prague, Czech Republic

    Miroslav Rada

Authors
  1. Elif Garajová
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  2. Miroslav Rada
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  3. Milan Hladík
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Corresponding author

Correspondence to Elif Garajová .

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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, Japan

    Van-Nam Huynh

  2. University of Hyogo, Kobe, Japan

    Tomoe Entani

  3. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Chawalit Jeenanunta

  4. Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka, Japan

    Masahiro Inuiguchi

  5. Sirindhorn International Institute of Technology, Thammasat University, Pathum Thani, Thailand

    Pisal Yenradee

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Garajová, E., Rada, M., Hladík, M. (2020). Outcome Range Problem in Interval Linear Programming: An Exact Approach. In: Huynh, VN., Entani, T., Jeenanunta, C., Inuiguchi, M., Yenradee, P. (eds) Integrated Uncertainty in Knowledge Modelling and Decision Making. IUKM 2020. Lecture Notes in Computer Science(), vol 12482. Springer, Cham. https://doi.org/10.1007/978-3-030-62509-2_1

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  • DOI: https://doi.org/10.1007/978-3-030-62509-2_1

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