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Analytic Hierarchy Process
Vikas Sao – vikas.sao@gmail.com
Vinit Modak – vinitmodak@gmail.com
Vinothkumar – p.vinok@gmail.com
Vipul Singh – vipulshipatul@gmail.com
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
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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)
SIOM | Symbiosis Institute of Operations Management, Nashik
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.
SIOM | Symbiosis Institute of Operations Management, Nashik
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
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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.
SIOM | Symbiosis Institute of Operations Management, Nashik
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
SIOM | Symbiosis Institute of Operations Management, Nashik
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)
SIOM | Symbiosis Institute of Operations Management, Nashik
Thank You
SIOM | Symbiosis Institute of Operations Management, Nashik

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Analytic Hierarchy Process AHP

  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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) SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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. SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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. SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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 SIOM | Symbiosis Institute of Operations Management, Nashik
  • 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) SIOM | Symbiosis Institute of Operations Management, Nashik
  • 19. Thank You SIOM | Symbiosis Institute of Operations Management, Nashik