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Fuzzy chance-constrained geometric programming: the possibility, necessity and credibility approaches

Author

Listed:
  • Rashed Khanjani Shiraz

    (University of Tabriz)

  • Madjid Tavana

    (La Salle University
    University of Paderborn)

  • Hirofumi Fukuyama

    (Fukuoka University)

  • Debora Di Caprio

    (York University
    Polo Tecnologico IISS G. Galilei)

Abstract

Geometric programming (GP) is a powerful tool for solving a variety of optimization problems. Most GP problems involve precise parameters. However, the observed values of the parameters in real-life GP problems are often imprecise or vague and, consequently, the optimization process and the related decisions take place in the face of uncertainty. The uncertainty associated with the coefficients of GP problems can be formalized using fuzzy variables. In this paper, we propose chance-constrained GP to deal with the impreciseness and the ambiguity inherent to real-life GP problems. Given a fuzzy GP model, we formulate three variants of chance-constrained GP based on the possibility, necessity and credibility approaches and show how they can be transformed into equivalent deterministic GP problems to be solved via the duality algorithm. We demonstrate the applicability of the proposed models and the efficacy of the introduced procedures with two numerical examples.

Suggested Citation

  • Rashed Khanjani Shiraz & Madjid Tavana & Hirofumi Fukuyama & Debora Di Caprio, 2017. "Fuzzy chance-constrained geometric programming: the possibility, necessity and credibility approaches," Operational Research, Springer, vol. 17(1), pages 67-97, April.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:1:d:10.1007_s12351-015-0216-7
    DOI: 10.1007/s12351-015-0216-7
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    References listed on IDEAS

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    1. Peter Kall & János Mayer, 2005. "Stochastic Linear Programming," International Series in Operations Research and Management Science, Springer, number 978-0-387-24440-2, September.
    2. TAVANA, Madjid & SHIRAZ, Rashed Khanjani & HATAMI-MARBINI, Adel & AGRELL, Per J., 2012. "Fuzzy stochastic data envelopment analysis with application to base realignment and closure (BRAC)," LIDAM Reprints CORE 2412, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    4. EMROUZNEJAD, Ali & TAVANA, Madjid & HATAMI-MARBINI, Adel, 2014. "The state of the art in fuzzy data envelopment analysis," LIDAM Reprints CORE 2543, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Wasim Akram Mandal, 2021. "Weighted Tchebycheff Optimization Technique Under Uncertainty," Annals of Data Science, Springer, vol. 8(4), pages 709-731, December.
    2. Rashed Khanjani-Shiraz & Salman Khodayifar & Panos M. Pardalos, 2021. "Copula theory approach to stochastic geometric programming," Journal of Global Optimization, Springer, vol. 81(2), pages 435-468, October.
    3. Zhang, Chenglong & Li, Xuemin & Guo, Ping & Huo, Zailin, 2021. "Balancing irrigation planning and risk preference for sustainable irrigated agriculture: A fuzzy credibility-based optimization model with the Hurwicz criterion under uncertainty," Agricultural Water Management, Elsevier, vol. 254(C).
    4. Wasim Akram Mandal & Sahidul Islam, 2017. "Multiobjective geometric programming problem under uncertainty," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 27(4), pages 85-109.
    5. Belleh Fontem, 2023. "Robust Chance-Constrained Geometric Programming with Application to Demand Risk Mitigation," Journal of Optimization Theory and Applications, Springer, vol. 197(2), pages 765-797, May.

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