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