1. An Illustrated Guide to
introducing
Analytic Hierarchy
Process

2. The Analytic Hierarchy Process (AHP)
• 1980 Saaty
•
multi-criteria decision making
•
•
–
–
–
2

3. AHP
•
• AHP 2
– Weight)
– Priorities)
• *
Weight, Priorities
3

4. :
•
–
•
– ,
–
•
– Honda Civic, Toyota Altis, Ford
Focus, Mazda 3
4

5. Hierarchy tree
S e lec ting
a N e w C ar
S tyle R e lia b ility F u e l E c on o m y
Civic Altis Focus Mazda3
5

6. •
1-9
•
– A
B 9
– B
A 1/9
•
7 !!!!! )
6

7. -
7

8. Ranking of criteria
1 1/2 3
2 1 4
1/3 1/4 1
8

9. Ranking of priorities
• Eigen Vector X:
1)
2)
Row
Normalized 0.30 0.29 0.38 0.30
1 0.5 3 Column Sums
averages
A= 2 1 4 0.60 0.57 0.50 0.60
X=
0.33 0.25 1.0 0.10 0.14 0.13 0.10
Priority vector
Column sums 3.33 1.75 8.00 1.00 1.00 1.00
9

10. Criteria weights
• .30
• .60
• .10
1.00
0.30 0.60 0.10
10

11. • Consistency Ratio (CR)
• (A > B) (B>C) (A > C)
• CR 0.1
11

12. Calculation of Consistency Ratio
• Weight (Eigen Vector)
• max (Ax)
Weight
A x Ax x
1 0.5 3 0.30 0.90 0.30
0.60 1.60 =
0.60
2 1 4 = max
0.10 0.35 0.10
0.333 0.25 1.0
λmax=average{0.90/0.30, 1.60/0.6, 0.35/0.10}=3.06
12

13. Calculation of Consistency Ratio
• Consistency Index (CI) = (λmax-n)/(n-1)
• Consistency Ratio (CR) = CI / random
index
– Random Index Table
• CI=(λmax-n)/(n-1)=(3.06-3)/(3-1)= 0.03
• CR = CI / RI(n)
• = 0.03 / 0.58 = 0.05

14. Ranking alternatives
Priority vector
Civic Altis Focus Mazda3
Civic 1 1/4 4 1/6 0.13
Altis 4 1 4 1/4 0.24
Focus 1/4 1/4 1 1/5 0.07
Mazda3 6 4 5 1 0.56
Civic Altis Focus Mazda3
Civic 1 2 5 1 0.38
Altis 1/2 1 3 2 0.29
Focus 1/5 1/3 1 1/4 0.07
0.26
Mazda3 1 1/2 4 1
14

15. Ranking alternatives
/ Normalized
Civic 34 .30
Altis 27 .24
Focus 24 .21
Mazda3 28 .25
113 1.0
:
15

16. Selecting a New Car
1.00
0.30 0.60 0.10
Civic 0.13 Civic 0.38 Civic 0.30
Altis 0.24 Altis 0.29 Altis 0.24
Focus 0.07 Focus 0.07 Focus 0.21
Mazda3 0.56 Mazda3 0.26 Mazda3 0.25
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17. Ranking of alternatives
Economy
Fuel
Civic .13 .38 .30 .30 .30
Altis .24 .29 .24 .27
x
.60 =
Focus .07 .07 .21 .08
Mazda3 .56 .26 .25 .10 .35
Priority matrix Criteria Weights
17

18. Methods for including cost criterion
•
40
Mazda3
35 Civic
30
Benefit
25
Altis
20
15 Focus
10
5
0
0 5 10 15 20 25 30 35
Cost
• cost/benefit ratios
• linear programming
• Decision Tree benefit cost
18

19. •
• Normalized 1
• Benefit
Normalized
• Cost/Benefits Ratio
Cost/Benefits
Cost Normalized Benefits Ratio
• CIVIC $12K .22 .30 0.73
• Altis $15K .28 .27 1.03
• Focus $9K .17 .08 2.13
• Mazda3 $18K .33 .35 0.92
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