Journal of Optimization Theory and Applications

, Volume 170, Issue 1, pp 243–265

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

  • Rashed Khanjani Shiraz
  • Madjid Tavana
  • Debora Di Caprio
  • Hirofumi Fukuyama
Article

DOI: 10.1007/s10957-015-0857-y

Cite this article as:
Khanjani Shiraz, R., Tavana, M., Di Caprio, D. et al. J Optim Theory Appl (2016) 170: 243. doi:10.1007/s10957-015-0857-y

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 

Mathematics Subject Classification

90C46 65K05 28B99 90C48 49K35 

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Rashed Khanjani Shiraz
    • 1
  • Madjid Tavana
    • 2
    • 3
  • Debora Di Caprio
    • 4
    • 5
  • Hirofumi Fukuyama
    • 6
  1. 1.School of Mathematics ScienceUniversity of TabrizTabrizIran
  2. 2.Distinguished Chair of Business Systems and Analytics, Business Systems and Analytics DepartmentLa Salle UniversityPhiladelphiaUSA
  3. 3.Business Information Systems Department, Faculty of Business Administration and EconomicsUniversity of PaderbornPaderbornGermany
  4. 4.Department of Mathematics and StatisticsYork UniversityTorontoCanada
  5. 5.Polo Tecnologico IISS G. GalileiBolzanoItaly
  6. 6.Faculty of CommerceFukuoka UniversityFukuokaJapan

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