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Posynomial Parametric Geometric Programming with Interval Valued Coefficient

Author

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  • G. S. Mahapatra

    (Siliguri Institute of Technology)

  • T. K. Mandal

    (D.I.B. High School)

Abstract

The article presents solution procedure of geometric programming with imprecise coefficients. We have considered problems with imprecise data as a form of an interval in nature. Many authors have solved the imprecise problem by geometric programming technique in a different way. In this paper, we introduce parametric functional form of an interval number and then solve the problem by geometric programming technique. The advantage of the present approach is that we get optimal solution of the objective function directly without solving equivalent transformed problems. Numerical examples are presented to support of the proposed approach.

Suggested Citation

  • G. S. Mahapatra & T. K. Mandal, 2012. "Posynomial Parametric Geometric Programming with Interval Valued Coefficient," Journal of Optimization Theory and Applications, Springer, vol. 154(1), pages 120-132, July.
    • Handle: RePEc:spr:joptap:v:154:y:2012:i:1:d:10.1007_s10957-012-9996-6
    DOI: 10.1007/s10957-012-9996-6
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    References listed on IDEAS

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    2. Liu, Shiang-Tai, 2006. "Posynomial geometric programming with parametric uncertainty," European Journal of Operational Research, Elsevier, vol. 168(2), pages 345-353, January.
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    7. Jung, Hoon & Klein, Cerry M., 2005. "Optimal inventory policies for an economic order quantity model with decreasing cost functions," European Journal of Operational Research, Elsevier, vol. 165(1), pages 108-126, August.
    8. H. C. Wu, 2010. "Duality Theory for Optimization Problems with Interval-Valued Objective Functions," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 615-628, March.
    9. Fang, S. C. & Peterson, E. L. & Rajasekera, J. R., 1988. "Controlled dual perturbations for posynomial programs," European Journal of Operational Research, Elsevier, vol. 35(1), pages 111-117, April.
    10. Elmor Peterson, 2001. "The Fundamental Relations between Geometric Programming Duality, Parametric Programming Duality, and Ordinary Lagrangian Duality," Annals of Operations Research, Springer, vol. 105(1), pages 109-153, July.
    11. Liu, Shiang-Tai, 2008. "Posynomial geometric programming with interval exponents and coefficients," European Journal of Operational Research, Elsevier, vol. 186(1), pages 17-27, April.
    12. Ji-hui Yang & Bing-yuan Cao, 2010. "Fuzzy geometric programming and its application," Fuzzy Information and Engineering, Springer, vol. 2(1), pages 101-112, March.
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    Cited by:

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    2. Gudivada Durga Bhavani & Ieva Meidute-Kavaliauskiene & Ghanshaym S. Mahapatra & Renata Činčikaitė, 2022. "Pythagorean Fuzzy Storage Capacity with Controllable Carbon Emission Incorporating Green Technology Investment on a Two-Depository System," Energies, MDPI, vol. 15(23), pages 1-34, November.

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