Issue: 2017/Vol.27/No.4, Pages 85-109
MULTIOBJECTIVE GEOMETRIC PROGRAMMING PROBLEM UNDER UNCERTAINTY
Wasim Akram Mandal
, Sahidul Islam
Cite as: W. A. Mandal, S. Islam. Multiobjective geometric programming problem under uncertainty. Operations Research and Decisions 2017: 27(4), 85-109. DOI 10.5277/ord170405
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.
Keywords: uncertainty theory, uncertain variable, linear, normal, zigzag uncertainty distribution, multiobjective geometric programming
Received: 27 June 2017 Accepted: 6 December 2017