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

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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.

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Acknowledgments

The authors would like to thank the anonymous reviewers and the editor for their insightful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics Science, University of Tabriz, Tabriz, Iran

    Rashed Khanjani Shiraz

  2. Distinguished Chair of Business Systems and Analytics, Business Systems and Analytics Department, La Salle University, Philadelphia, PA, 19141, USA

    Madjid Tavana

  3. Business Information Systems Department, Faculty of Business Administration and Economics, University of Paderborn, 33098, Paderborn, Germany

    Madjid Tavana

  4. Department of Mathematics and Statistics, York University, Toronto, M3J 1P3, Canada

    Debora Di Caprio

  5. Polo Tecnologico IISS G. Galilei, Via Cadorna 14, 39100, Bolzano, Italy

    Debora Di Caprio

  6. Faculty of Commerce, Fukuoka University, Fukuoka, Japan

    Hirofumi Fukuyama

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  1. Rashed Khanjani Shiraz
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  2. Madjid Tavana
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  3. Debora Di Caprio
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  4. Hirofumi Fukuyama
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Correspondence to Madjid Tavana.

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Khanjani Shiraz, R., Tavana, M., Di Caprio, D. et al. Solving Geometric Programming Problems with Normal, Linear and Zigzag Uncertainty Distributions. J Optim Theory Appl 170, 243–265 (2016). https://doi.org/10.1007/s10957-015-0857-y

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  • DOI: https://doi.org/10.1007/s10957-015-0857-y

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