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

Rashed Khanjani Shiraz (), Madjid Tavana (), Debora Di Caprio () and Hirofumi Fukuyama ()
Additional contact information
Rashed Khanjani Shiraz: University of Tabriz
Madjid Tavana: La Salle University
Debora Di Caprio: York University

Journal of Optimization Theory and Applications, 2016, vol. 170, issue 1, No 15, 243-265

Abstract: 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.

Keywords: Uncertainty theory; Uncertain variable; Linear uncertainty distribution; Normal uncertainty distribution; Zigzag uncertainty distribution; 90C46; 65K05; 28B99; 90C48; 49K35 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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DOI: 10.1007/s10957-015-0857-y

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