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.

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.

exampleGraphical 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


The problem is graphed in the following figure.

Graphical Method, Goal Programming, Examples

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

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