Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ-constraint method along with Karush-Kuhn-Tucker (KKT) condition has been used to solve multi-objective Geometric programming problems(MOGPP) for searching a compromise solution. To find the suitable compromise solution for multi-objective Geometric programming problems, a brief solution procedure using ϵ-constraint method has been presented. The basic concept and classical principle of multi-objective optimization problems with KKT condition has been discussed. The result obtained by ϵ-constraint method with help of KKT condition has been compared with the result so obtained by Fuzzy programming method. Illustrative examples are presented to demonstrate the correctness of proposed model.

Keywords: geometric programming, Karush-Kuhn-Tucker (KKT) condition, ϵ-constraint method, fuzzy programming, duality theorem, Pareto optimal solution

@article{RO_2014__48_4_429_0, author = {Ojha, A. K. and Ota, Rashmi Ranjan}, title = {Multi-objective geometric programming problem with {Karush-Kuhn-Tucker} condition using $\varepsilon $-constraint method}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {429--453}, publisher = {EDP-Sciences}, volume = {48}, number = {4}, year = {2014}, doi = {10.1051/ro/2014016}, zbl = {1299.90297}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ro/2014016/} }

TY - JOUR AU - Ojha, A. K. AU - Ota, Rashmi Ranjan TI - Multi-objective geometric programming problem with Karush-Kuhn-Tucker condition using $\varepsilon $-constraint method JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 429 EP - 453 VL - 48 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ro/2014016/ DO - 10.1051/ro/2014016 LA - en ID - RO_2014__48_4_429_0 ER -

%0 Journal Article %A Ojha, A. K. %A Ota, Rashmi Ranjan %T Multi-objective geometric programming problem with Karush-Kuhn-Tucker condition using $\varepsilon $-constraint method %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 429-453 %V 48 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ro/2014016/ %R 10.1051/ro/2014016 %G en %F RO_2014__48_4_429_0

Ojha, A. K.; Ota, Rashmi Ranjan. Multi-objective geometric programming problem with Karush-Kuhn-Tucker condition using $\varepsilon $-constraint method. RAIRO - Operations Research - Recherche Opérationnelle, Volume 48 (2014) no. 4, pp. 429-453. doi : 10.1051/ro/2014016. http://archive.numdam.org/articles/10.1051/ro/2014016/

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