Introduction to Goal Programming
• Multiple conflicting objectives
–Reduce national debt
–Income tax relief
• Obtain compromise solution
• Try to “satisfy” goals rather than optimize
Goal
- an objective in conjunction with an aspiration level
Examples:
– Achieve at least $20,000 in profit
– Reduce emissions by 50%
Goal Deviation
difference between what is
aspired to and what is accomplished with
objective
Visualize Goal Deviation with slack
Goals act as constraints in the GP
– Advantages
– Allows multiple objectives
– Allows slack in the constraint (not hard)
Goals act as constraints in the GP
– Disadvantages
– Complexity of the “overall objective”
– Must elicit goal values (and weights) from Decision Maker
– Must find a way to homogenize these values
Solving Goal Programs
• Weights Method
• Preemptive Method
• Taha’s Method
Weights Method
• Single objective function is the weighted sum of the functions representing the goals
min z = w1G1 + w2G2 +...+ wnGn
Preemptive Method
• Prioritize goals in order of importance
• Model optimized with one goal at a time
–Higher priority goal never degraded by lower priority goal
Steps in Taha's Approach
Step 0: Rank goals in order of priority
Step 1: Solve LP that minimizes Gi
Taha's Approach Step 0: Rank goals in order of priority
G1 = p1>G2 = p2>...Gn = pn
s
-set i = 1
Taha's Approach Step 1: Solve LP that minimizes Gi
– pi = pi* denotes optimum value of deviational variable
– If i = n, stop
– Else, add constraint to the constraints of the Gi problem to ensure value of ri not degraded in future problems
• Seti=i+1
Formulation
Solve LP1
Solve LP2