1. Analytic Hierarchy Process
Vikas Sao – vikas.sao@gmail.com
Vinit Modak – vinitmodak@gmail.com
Vinothkumar – p.vinok@gmail.com
Vipul Singh – vipulshipatul@gmail.com

2. Introduction
• Developed by T. Saaty
• Best known and widely used Multi Criteria Analysis (MCA) approach
• Relative priority of each criteria
• Real world decision problems
• Spend on Defence or Agriculture?
• Buy an Ecosport or Koleos?
• Integrated manufacturing (Putrus, 1990),
• In the evaluation of technology investment decisions (Boucher and McStravic,
1991)
• In flexible manufacturing systems (Wabalickis, 1988)
• Layout design (Cambron and Evans, 1991)
SIOM | Symbiosis Institute of Operations Management, Nashik

3. History
• AHP first introduced by Saaty in 1977
• Apparent problems with the way pairwise comparisons were used pointed
out by Belton and Gear in 1983
• Belton and Gear introduced Revised-AHP
• Saaty accepted the change and introduced Ideal Mode AHP in 1994
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4. Procedure
• Structure a decision problem and selection of criteria
• Priority setting of the criteria by pairwise comparison (WEIGHING)
• Pairwise comparison of options on each criterion (SCORING)
• Obtaining an overall relative score for each option
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5. Structuring a decision problem and
selection of criteria
• Divide the problem into its constituent parts
• Goal at the Topmost Level
• Criteria at the Intermediate Level
• Options at the Lowest Level
• What it does?
• Provides an overall view of the complex
relationships
• Access whether the element in each level are of
the same magnitude to compare accurately
Selecting
a Car
Style Reliability Mileage
Ecosport (E) Koleos (K) Scorpio (S) Duster (D)
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6. Ranking of Criteria and Alternatives
• Pairwise comparisons are made with the grades ranging from
1-9.
• A basic, but very reasonable assumption for comparing
alternatives:
If attribute A is absolutely more important than attribute B and is rated at 9,
then B must be absolutely less important than A and is graded as 1/9.
• These pairwise comparisons are carried out for all factors to be
considered, usually not more than 7, and the matrix is
completed.
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7. Priority setting of the criteria
by pairwise comparison
(WEIGHING)
• How important is criterion A relative to criterion B?
• Assign a weight between 1 and 9
• Reciprocal of the value is assigned to the other
criterion in the pair
• How important is criterion B relative to criterion A?
• Normalize and average the weighing to obtain
average weight for each criterion
9
Extreme
Importance
1
Equal
Importance
Scale Definition Explanation
1 Equal
importance
Two activities contribute
equally to the objective
3 Weak
importance of
one over
another
Experience and judgment
slightly favour one activity
over another
5 Essential or
strong
importance
Experience and judgment
strongly favour one
activity over another
7 Demonstrated
importance
An activity is strongly
favoured and its
dominance demonstrated
in practice
9 Absolute
importance
The evidence favoring one
activity over another is of
the highest possible
order of affirmation
2,4,6,8 Intermediate
values
between the
two
adjacent
judgments
When compromise is
needed
SIOM | Symbiosis Institute of Operations Management, Nashik

8. Priority setting of the criteria
by pairwise comparison
(WEIGHING)
Scale Definition Explanation
1 Equal
importance
Two activities contribute
equally to the objective
3 Weak
importance of
one over
another
Experience and judgment
slightly favour one activity
over another
5 Essential or
strong
importance
Experience and judgment
strongly favour one
activity over another
7 Demonstrated
importance
An activity is strongly
favoured and its
dominance demonstrated
in practice
9 Absolute
importance
The evidence favoring one
activity over another is of
the highest possible
order of affirmation
2,4,6,8 Intermediate
values
between the
two
adjacent
judgments
When compromise is
needed
STYLE RELIABILITY MILEAGE
STYLE 1 1/2 3
RELIABILITY 2 1 4
MILEAGE 1/3 1/4 1
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9. Priority setting of the criteria
by pairwise comparison
(WEIGHING)
STYLE RELIABILITY MILEAGE G.M. EIGEN
VECTOR
STYLE
1 1/2 3 1.14 0.3196
RELIABILITY
2 1 4 2.00 0.5584
MILEAGE
1/3 1/4 1 0.44 0.1220
SUM
3.33 1.75 8 3.58
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10. 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.
0.3196
0.5584
0.1220
1 0.5 3
2 1 4
0.333 0.25 1.0
0.9648
1.6856
0.3680
= = max
λmax=average{0.9648/0.3196, 1.6856/0.5584, 0.3680/0.1220}=3.0180
0.3196
0.5584
0.1220
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11. Consistency Index
• The final step is to calculate the Consistency Ratio.
• CI=(max –n)/(n-1)
• CR=CI/RI=0.0090/0.58=0.01552
less than 0.1 so the evaluations are consistent
• An inconsistency of 10% or less implies that the adjustment is small
compared to the actual values of the eigenvector entries.
• A CR as high as, say, 90% would mean that the pairwise judgment are just
about random and are completely untrustworthy
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12. Pairwise comparison of options on each
criterion (SCORING)
• Using Pairwise Comparisons, the Relative Importance Of One Criterion Over
Another can be expressed.
E K S D
E 1 1/4 4 1/6
K 4 1 4 1/4
S 1/4 1/4 1 1/5
D 6 4 5 1
Km / L
E 34
K 27
S 24
D 28
E K S D
E 1 2 5 1
K 1/2 1 3 2
S 1/5 1/3 1 1/4
D 1 1/2 4 1
STYLE RELIABILITY MILEAGE
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13. 3.00 1.75 8.00
5.33 3.00 14.0
1.17 0.67 3.00
A2=
Row sums
12.75
22.33
4.83
39.92
Normalized Row Sums
0.3194
0.5595
0.1211
1.0
Iteration 1:
Initialization:
A2xA2=
27.67 15.83 72.50
48.33 27.67 126.67
10.56 6.04 27.67
A=
1 0.5 3
2 1 4
0.33 0.25 1.0
Row sums
12.75
22.33
4.83
39.92
Normalized Row Sums
0.3196
0.5584
0.1220
0.0002
-0.0011
0.0009
E1-E0 = -
0.3194
0.5595
0.1211
0.3196
0.5584
0.1220
=
Almost zero, so
Eigen Vector, X = E1.
E0
E1
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14. Pairwise comparison of options on each
criterion (SCORING)
• Using Pairwise Comparisons, the Relative Importance Of One Criterion Over
Another can be expressed.
Km / L E.V
E 34 0.3010
K 27 0.2390
S 24 0.2120
D 28 0.2480
STYLE RELIABILITY MILEAGE
E K S D E.V.
E 1.00 0.25 4.00 0.17 0.1160
K 4.00 1.00 4.00 0.25 0.2470
S 0.25 0.25 1.00 0.20 0.0600
D 6.00 4.00 5.00 1.00 0.5770
E K S D E.V
E 1.00 2.00 5.00 1.00 0.3790
K 0.50 1.00 3.00 2.00 0.2900
S 0.20 0.33 1.00 0.25 0.0740
D 1.00 0.50 4.00 1.00 0.2570
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15. Obtaining an overall relative score for each
option
• The option scores are combined with the criterion weights to produce an
overall score for each option.
Final Ranking Of Alternatives = Ranking Of Alternative (Category
Wise)*Criteria Weights
E
D
S
K
.1160 .3790 .3010
.2470 .2900 .2390
.0600 .0740 .2120
.5770 .2570 .2480
*
.3196
.5584
.1220
=
.2854
.2700
.0864
.3582
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16. In the industry
Areas Company Application
Choice Xerox Product selection
Prioritization General Motors Prioritizing the design alternatives and arrive at a
cost effective design
Resource Allocation Korea
Telecommunication
Authority
Allocation of R&D Budget for 10 technologies
Benchmarking IBM Compare IBM CIM with best of breed companies
Quality Management Steel & Magnetic
Division, Italy
Comparison with its competitors and improve the
quality
Public policy Japan Formulate policy to maintain Sea of Japan
Health care Medical Center,
Washington
Type of team to be sent in case of different
disaster
Strategic Planning 3M A computerized AHP for quick evaluation of
strategy.
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17. AHP with feedback
• Priorities of elements in a level is not dependent on the lower level
elements. NOT ALWAYS TRUE
• GOAL : Construction of bridge
• CRITERIA : STRENGTH, COST, LOOK
• OPTIONS : A,B
• A – MEETS ALL THE STRENGTH REQUIREMENTS, LOOKS BEAUTIFUL
• B – MOST STRONGEST, EQUAL COST, UGLY
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18. WEB BASED
• http://www.isc.senshu-u.ac.jp/~thc0456/EAHP/AHPweb.htm
• Input
• Size of pairwise comparison Matrix
• Pairwise comparison Matrix
• Output
• Eigen Vector
• Consistency Index
• www.superdecisions.com
• Provide software for AHP and ANP
• Exhaustive tutorials (PDF and Video)
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19. Thank You
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