Civil Infrastructure Systems-Module 6

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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

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Solve LP1

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Solve LP2

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