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Multiobjective geometric programming problem under uncertainty

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  • Wasim Akram Mandal
  • Sahidul Islam

Abstract

Multiobjective geometric programming (MOGP) is a powerful optimization technique widely used for solving a variety of nonlinear optimization problems and engineering problems. Generally, the parameters of a multiobjective geometric programming (MOGP) models are assumed to be deterministic and fixed. However, the values observed for the parameters in real-world MOGP problems are often imprecise and subject to fluctuations. Therefore, we use MOGP within an uncertainty based framework and propose a MOGP model whose coefficients are uncertain in nature. We assume the uncertain variables (UVs) to have linear, normal or zigzag uncertainty distributions and show that the corresponding uncertain chance-constrained multiobjective geometric programming (UCCMOGP) problems can be transformed into conventional MOGP problems to calculate the objective values. The paper develops a procedure to solve a UCCMOGP problem using an MOGP technique based on a weighted-sum method. The efficacy of this procedure is demonstrated by some numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:wut:journl:v:4:y:2017:p:85-109:id:1323
    DOI: 10.5277/ord170405
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    References listed on IDEAS

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    1. 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(3), pages 1075-1078, September.
    2. Yang, Hsu-Hao & Bricker, Dennis L., 1997. "Investigation of path-following algorithms for signomial geometric programming problems," European Journal of Operational Research, Elsevier, vol. 103(1), pages 230-241, November.
    3. 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.
    4. 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.
    5. Li, Shengguo & Peng, Jin & Zhang, Bo, 2013. "The uncertain premium principle based on the distortion function," Insurance: Mathematics and Economics, Elsevier, vol. 53(2), pages 317-324.
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    Cited by:

    1. Mustapha Kaci & Sonia Radjef, 2023. "An adaptive method to solve multilevel multiobjective linear programming problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 33(3), pages 29-44.

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