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.