Goal Programming

Example 2

Minimize z = P₁d₁^- + 2P₂d₂^- + P₂d₃^- + P₃d₁⁺

subject to

x₁ + x₂ + d₁^- - d₁⁺ = 350
x₁ + d₂^- = 200
x₂ + d₃^- = 300

x₁, x₂, d₁^-, d₂^-, d₃^-, d₁⁺ ³ 0

Solution.

Substituting x₁ = 0, x₂ = 0, d₁⁺ = 0
Therefore, d₁^- = 350, d₂^- = 200, d₃^- = 300

Table 1

Key column = x₁ column
Minimum positive value = Min(350/1, 200/1) = 200
So, d₂^- row is the key row.
Therefore, d₂^- departs & x₁ enters

Table 2

Table 3

Table 4

The optimal solution is:
x₁ = 200, x₂ = 300, d₁^- = 0, d₂^- = 0, d₃^- = 0, d₁⁺ = 150.

Goal programming is a powerful tool to tackle multiple and incompatible goals of an enterprise. It is becoming popular because of its applicability in solving a wide range of problems in diversified areas. The most important advantage of goal programming is its great flexibility, which allows model simulation with numerous variation of constraints and goal priorities. This chapter discussed the solution of a goal programming problem by using the graphical method and simplex method.