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Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions

Author

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  • Rashed Khanjani Shiraz

    (University of Tabriz)

  • Madjid Tavana

    (La Salle University
    University of Paderborn)

  • Debora Di Caprio

    (York University
    Polo Tecnologico IISS G. Galilei)

  • Hirofumi Fukuyama

    (Fukuoka University)

Abstract

Geometric programming is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Conventional geometric programming models assume deterministic and precise parameters. However, the values observed for the parameters in real-world geometric programming problems often are imprecise and vague. We use geometric programming within an uncertainty-based framework proposing a chance-constrained geometric programming model whose coefficients are uncertain variables. We assume the uncertain variables to have normal, linear and zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained geometric programming problems can be transformed into conventional geometric programming problems to calculate the objective values. The efficacy of the procedures and algorithms is demonstrated through numerical examples.

Suggested Citation

  • Rashed Khanjani Shiraz & Madjid Tavana & Debora Di Caprio & Hirofumi Fukuyama, 2016. "Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 243-265, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-015-0857-y
    DOI: 10.1007/s10957-015-0857-y
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    Cited by:

    1. Huang, Xiaoxia & Ma, Di & Choe, Kwang-Il, 2023. "Uncertain mean–variance portfolio model with inflation taking linear uncertainty distributions," International Review of Economics & Finance, Elsevier, vol. 87(C), pages 203-217.
    2. Wasim Akram Mandal, 2021. "Weighted Tchebycheff Optimization Technique Under Uncertainty," Annals of Data Science, Springer, vol. 8(4), pages 709-731, December.
    3. Tingting Yang & Xiaoxia Huang, 2022. "A New Portfolio Optimization Model Under Tracking-Error Constraint with Linear Uncertainty Distributions," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 723-747, November.
    4. 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.
    5. Dennis L. Bricker & K. O. Kortanek, 2017. "Perfect Duality in Solving Geometric Programming Problems Under Uncertainty," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 1055-1065, June.
    6. 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.
    7. 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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