Research Article

Two Weighted Fuzzy Goal Programming Methods to Solve Multiobjective Goal Programming Problem

Table 12

Solution of the FLGP problem by varying the resource of the first constraint.

𝑏 1 Weight ( 𝑤 )Proposed method 1Proposed method 2

𝑏 1 = 8 1 , 1 No feasible solutionNo feasible solution
𝑤 < 1 No feasible solutionNo feasible solution
𝑏 1 = 9 1 , 1 𝑍 1 = 6 , 𝑍 2 = 3 , 𝜆 = . 6 6 𝑍 1 = 6 , 𝑍 2 = 3 , 𝜆 = . 6 6
𝑤 < 1 𝑍 1 = 9 , 𝑍 2 = 3 , 𝜆 = 1 𝑍 1 = 9 , 𝑍 2 = 3 , 𝜆 = . 3 3
𝑏 1 = 1 0 1 , 1 𝑍 1 = 9 , 𝑍 2 = 4 , 𝜆 = 1 𝑍 1 = 9 , 𝑍 2 = 4 , 𝜆 = 1
𝑤 < 1 𝑍 1 = 9 , 𝑍 2 = 3 , 𝜆 = 1 𝑍 1 = 9 . 5 , 𝑍 2 = 4 , 𝜆 = 1
𝑏 1 = 1 1 1 , 1 𝑍 1 = 9 , 𝑍 2 = 4 , 𝜆 = 1 𝑍 1 = 9 , 𝑍 2 = 4 , 𝜆 = 1
𝑤 < 1 𝑍 1 = 9 , 𝑍 2 = 3 , 𝜆 = 1 𝑍 1 = 1 0 . 5 , 𝑍 2 = 4 , 𝜆 = 1