Optimization is an important tool widely used in formulation of the mathematical modeland 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 andmulti-choice with certain constraints. There is no such single optimal solution existwhich could optimize all the objective functions simultaneously. In this paper,ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used tosolve multi-objective Geometric programming problems(MOGPP) for searching a compromisesolution. To find the suitable compromise solution for multi-objective Geometricprogramming problems, a brief solution procedure using ϵ-constraint method hasbeen presented. The basic concept and classical principle of multi-objective optimizationproblems with KKT condition has been discussed. The result obtained by ϵ-constraint method withhelp of KKT condition has been compared with the result so obtained by Fuzzy programmingmethod. Illustrative examples are presented to demonstrate the correctness of proposedmodel.

Consider a fixed set of n events. Let S1 denote the sum of the probabilities of occurrence of each event and S2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S1 and S2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).