The document describes the Analytic Hierarchy Process (AHP), which is a structured technique for organizing and analyzing complex decisions. AHP involves constructing a hierarchy of criteria and alternatives, then making pairwise comparisons between elements to determine their relative importance. These comparisons are used to calculate weights for criteria and priorities for alternatives. The document provides an example of using AHP to select a car based on style, reliability, and fuel economy criteria. It also outlines the steps to determine criteria weights, alternative priorities, and consistency ratios in AHP.

1. Analytic Hierarchy Process
By: Aman Kumar Gupta
(2012MB31)
1

2. Table of Content
•
•
•
•
•
What is AHP
General Idea
Example: Car Selection
Ranking Scale for Criteria and Alternatives
Pros and Cons of AHP
2

3. Analytic Hierarchy Process(AHP)
• The Analytic Hierarchy Process (AHP) is a structured
technique for organizing and analyzing complex
decisions.
• It was developed by Thomas L. Saaty in the 1970s.
• Application in group decision making.
3

4. Analytic Hierarchy Process (Cont.)
Wide range of applications exists:
•
Selecting a car for purchasing
•
Deciding upon a place to visit for vacation
•
Deciding upon an MBA program after graduation.
4

5. General Idea
AHP algorithm is basically composed of two steps:
1. Determine the relative weights of the decision criteria
2. Determine the relative rankings (priorities) of alternatives
Both qualitative and quantitative information can be
compared by using informed judgments to derive weights
and priorities.
5

6. Example: Car Selection
•
Objective
•
•
Criteria
•
•
Selecting a car
Style, Reliability, Fuel-economy
Cost?
Alternatives
•
Civic Coupe, Saturn Coupe, Ford Escort, Mazda
Miata
6

7. Hierarchy tree
Selecting
a New Car
Style
Civic
Reliability
Saturn
Fuel Economy
Escort
Alternative courses of action
Miata
7

8. Ranking Scale for Criteria and
Alternatives
http://en.wikipedia.org/wiki/Talk:Analytic_Hier
archy_Process/Example_Car
8

9. Ranking of criteria
Style
Reliability
Fuel Economy
Style
1
1/2
3
Reliability
2
1
4
1/3
1/4
1
Fuel Economy
9

10. Ranking of priorities
• Consider [Ax = maxx] where
• A is the comparison matrix of size n n, for n criteria, also called the priority matrix.
• x is the Eigenvector of size n 1, also called the priority vector.
• max is the Eigenvalue.
• To find the ranking of priorities, namely the Eigen Vector X:
1) Normalize the column entries by dividing each entry by the sum of the column.
2) Take the overall row averages.
A=
1
0.5 3
2
1
4
0.33 0.25 1.0
Column sums 3.33 1.75
8.00
Normalized
Column Sums
0.30
0.60
0.10
0.28
0.57
0.15
0.37
0.51
0.12
1.00
1.00
1.00
Row
averages
X=
0.32
0.56
0.12
Priority vector
10

11. Criteria weights
• Style
.32
• Reliability
.56
• Fuel Economy .12
Selecting a New Car
1.00
Style
0.32
Reliability
0.56
Fuel Economy
0.12
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12. Checking for Consistency
• The next stage is to calculate a Consistency Ratio (CR) to
measure how consistent the judgments have been relative
to large samples of purely random judgments.
• AHP evaluations are based on the aasumption that the
decision maker is rational, i.e., if A is preferred to B and
B is preferred to C, then A is preferred to C.
• If the CR is greater than 0.1 the judgments are
untrustworthy because they are too close for comfort to
randomness and the exercise is valueless or must be
repeated.
12

13. Calculation of Consistency Ratio
• The next stage is to calculate max so as to lead to the
Consistency Index and the Consistency Ratio.
• Consider [Ax = max x] where x is the Eigenvector.
A
1
0.5
2
1
0.333 0.25
x
3
4
1.0
Ax
x
0.32
0.56
0.12
0.98
1.68
0.36
0.32
0.56
0.12
=
=
max
λmax=average{0.98/0.32, 1.68/0.56, 0.36/0.12}=3.04
Consistency index , CI is found by
CI=(λmax-n)/(n-1)=(3.04-3)/(3-1)= 0.02
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14. C.R. = C.I./R.I. where R.I. is the random index
n 1
2
3
4
5
6
R.I.
0
0
.52
.88
1.11 1.25
7
1.35
C.I. = 0.02
n=3
R.I. = 0.50(from table)
So, C.R. = C.I./R.I. = 0.02/0.52 = 0.04
C.R. ≤ 0.1 indicates sufficient consistency for decision.
14

15. Ranking alternatives
Style
Civic
Civic
1
Saturn
4
1
4
1/4
Escort
Miata
1/4
6
1/4
4
1
5
1/5
1
Reliability Civic
Saturn
1/4
Saturn
2
Escort Miata
4
1/6
Escort Miata
5
1
Civic
1
Saturn
Escort
1/2
1/5
1
1/3
3
1
2
1/4
Miata
1
1/2
4
1
Priority vector
0.13
0.24
0.07
0.56
0.38
0.29
0.07
0.26
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16. Ranking alternatives
Miles/gallon
Priority Vector
Civic
34
.30
Saturn
Escort
Miata
Fuel Economy
27
24
28
113
.24
.21
.25
1.0
Since fuel economy is a quantitative measure, fuel
consumption ratios can be used to determine the
relative ranking of alternatives.
16

17. Selecting a New Car
1.00
Style
0.32
Civic
Saturn
Escort
Miata
0.13
0.24
0.07
0.56
Reliability
0.56
Civic
Saturn
Escort
Miata
0.38
0.29
0.07
0.26
Fuel Economy
0.12
Civic
Saturn
Escort
Miata
0.30
0.24
0.21
0.25
17

18. Fuel
Economy
Reliability
Style
Ranking of alternatives
Civic
.13 .38 .30
Saturn
Escort
.24 .29 .24
Miata
.56 .26 .25
.07 .07 .21
Priority matrix
.32
x
.56
.12
.28
.25
=
.07
.34
Criteria Weights
18

19. Including Cost as a Decision Criteria
Adding “cost” as a a new criterion is very difficult in AHP. A new column and a
new row will be added in the evaluation matrix. However, whole evaluation
should be repeated since addition of a new criterion might affect the relative
importance of other criteria as well!
Instead one may think of normalizing the costs directly and calculate the
cost/benefit ratio for comparing alternatives!
Cost
•
•
•
•
CIVIC
SATURN
ESCORT
MIATA
Normalized
Cost
Benefits
Cost/Benefits
Ratio
$ 12k
$15K
$9K
$18K
.22
.28
.17
.33
.28
.25
.07
.34
0.78
1.12
2.42
0.97
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20. • The “ESCORT” Is the winner with the highest benefit to
COST RATIO and we rank it 1st ,
• Then at 2nd position Saturn,
• At 3rd Miata,
• At 4th Civic.
20

21. More about AHP: Pros and Cons
Pros
• It allows multi criteria decision making.
• It is applicable when it is difficult to formulate criteria
evaluations, i.e., it allows qualitative evaluation as well as
quantitative evaluation.
• It is applicable for group decision making environments
Cons
•There are hidden assumptions like consistency.
Repeating evaluations is cumbersome.
•Difficult to use when the number of criteria or
alternatives is high, i.e., more than 7.
•Difficult to add a new criterion or alternative
•Difficult to take out an existing criterion or alternative,
since the best alternative might differ if the worst one is
excluded.
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