Goal Programming

Graphical Method

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.

The graphical method is not appropriate for solving real large scale problems; however, the pictorial interpretation will help you in developing intuition about the workings of a goal programming model.

Example

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⁺ ³ 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