Graphical Method: Goal Programming

This section deals with geometric representation of a goal programming problem. The graphical method of solving goal programming problem is quite similar to the graphical method of linear programming.

Graphical Method Example: Goal Programming

Minimize z = P₁d₁⁻ + 2P₂d₂⁻ + P₂d₃⁻ + P₃d₁⁺

subject to

x₁ + x₂ + d₁⁻  - d₁⁺ = 450
x₁ + d₂⁻ = 250
x₂ + d₃⁻ = 350

x₁, x₂, d₁⁻, d₂⁻, d₃⁻, d₁⁺ ≥ 0

Solution.

The problem is graphed in the following figure.

The region bounded by OPQR represents the solution set.

The optimal solution to the problem is given below:
x₁ = 250, x₂ = 350, d₁⁻ = 0, d₂⁻ = 0, d₃⁻ = 0, d₁⁺ = 150