1. Quantitative Analysis for Management Multifactor Evaluation Process and Analytic Hierarchy Process Dr. Mohammad T. Isaai Graduate School of Management & Economics Sharif University of Technology

2. Multifactor Evaluation Process (MFEP)
Assume you have to select among some alternatives
To evaluate each alternative, some factors are considered.
For example, someone intends to buy a house; then, the factors can be price, location, distance to their workplace, neighborhood etc.
Two types of evaluation is required:
Factor Weight
Alternative Evaluation
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3. The Decision-Making Process:
Identify Problem
Select Alternative
Develop Decision
Criteria
Allocate Weights
to Criteria
Implement
Alternative
Develop
Alternatives
Analyze
Alternatives
Evaluate Results

4. Quantitative Analysis for Management
MFEP Example
someone decides to buy one of the following cars: A B C D
There are three factors to consider:
Style
Reliability
Fuel Economy
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5. Quantitative Analysis for Management
Factor Weights
From decision maker’s point of view, importance weight of the factors are:
Style 0.5
Reliability 0.3
Fuel Economy 0.2
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6. Alternative Evaluation
Car
Factor A B C D
Style
0.1
0.3
0.5
Reliability
0.4
0.2
Fuel Economy
The Results
A: 0.1* * *0.2= 0.21
B: * * *0.2= 0.28
C: 0.1* * *0.2= 0.18
D: * * *0.2= 0.33
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7. Analytic Hierarchy Process (AHP)
The difficulty with traditional MFEP is the evaluation approach. It is usually difficult or even impossible to evaluate all alternatives, especially when there are too many.
The AHP, developed by Tom Saaty in 1980, is a decision-making method for prioritizing alternatives when multi-criteria must be considered.
AHP is based on two concepts:
Hierarchy Design
Pair-wise Comparisons
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8. Quantitative Analysis for Management
Comparisons
How does AHP capture human judgments?
AHP never requires you to make an absolute judgment or assessment. You would never be asked to directly estimate the weight of a stone in kilograms.
AHP does require you to make a relative assessment between two items at a time. AHP uses a ratio scale of measurement.
For example, if there are four cars and you want to evaluate their Appearance . Clearly it is difficult to evaluate them absolutely.
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9. Pair-wise Comparisons
However, it is easy to compare any two of them.
The question is how do you prefer car A to car B, as far as the appearance is concerned.
The reply may be “I prefer it strongly” or “I prefer it moderately”
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10. AHP Pair-wise Comparison Scale
Numerical Ratings Verbal Description of Judgment
Equally preferred
Moderately preferred
Strongly preferred
Very strongly preferred
Extremely strongly preferred
We may also use numerical ratings 2, 4, 6 and 8. They describe something between two ratings.
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11. Quantitative Analysis for Management
Complete AHP Scale
Numerical Verbal Description of
Ratings Judgement
Equally preferred
Equally to moderate preferred
Moderately preferred
Moderately to strongly preferred
Strongly preferred
Strongly to very strongly preferred
Very strongly preferred
Very strongly to extremely strongly pr
Extremely strongly preferred
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12. Quantitative Analysis for Management
Hierarchy Structure
AHP problems are structured in at least three levels:
The goal, such as selecting the best car to purchase,
The criteria, such as style, Reliability, and Fuel Economy,
The alternatives, namely the cars themselves.
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13. Example: Car Selection
Objective
Selecting a car
Criteria
Style, Reliability, Fuel-economy Cost?
Alternatives
Civic Coupe, Saturn Coupe, Ford Escort, Mazda Miata
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14. Quantitative Analysis for Management
Hierarchical tree
Level 1: Goals
Level 2: Criteria
- Civic
- Saturn
- Escort
- Miata
- Civic
- Saturn
- Escort
- Miata
- Civic
- Saturn
- Escort
- Miata
Level 3: Alternatives
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15. Quantitative Analysis for Management
First, we deal with
FACTOR WEIGHTS
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16. Pair-wise Comparisons
Q: How important is Style with respect to Fuel Economy?
A: Moderately Important. Then numerical rating is 3
As a result the importance of Fuel Economy with respect to Style is 1/3.
This type of comparison continues for every pair of factors
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17. Pair-wise Comparisons
Similarly Reliability with respect to style is equally to moderately important (Rating=2).
Reliability with respect to fuel economy is moderately to strongly important (Rating=4).
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18. Pair-wise Comparisons Matrix
Clearly, each factor is as important as itself. Then, all diagonal entries are equal to 1.
The criteria matrix is as follows.
Style
Reliability
Fuel Economy
1 1/2 3
1/3 1/4 1
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19. Quantitative Analysis for Management
Ranking the Factors-1
Step 1. Normalize each column, i.e. divide the elements of each column by its total.
Factors
Style
Rel.
F.E 1
0.5 3 2 4
F.E.
0.33
0.25
Total
3.33
1.75 8
Factors
Style
Rel.
F.E
0.3
0.285
0.375
0.6
0.57
0.5
F.E.
0.1
0.145
0.125
Total 1
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20. Quantitative Analysis for Management
Ranking the Factors-2
Step 2. Calculate Factor Weights.
Factors
Style
Rel.
F.E
Average
0.3
0.285
0.375
( )/3=
0.6
0.57
0.5
( )/3=
F.E.
0.1
0.145
0.125
( )/3=
Total 1
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21. Quantitative Analysis for Management
Preference
Style
Reliability
Fuel Economy
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22. Quantitative Analysis for Management
Second, we deal with
Alternative Evaluations
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23. Quantitative Analysis for Management
Ranking alternatives
Average
Style
Civic
Saturn
Escort
Miata
Civic
/ /6
.1160
.2470
.0600
.5770
Saturn /4
Escort
1/ / /5
Miata
Reliability
Civic
Saturn
Escort
Miata
Civic
1/ /1 5/ /1
.3790
.2900
.0740
.2570
Saturn
1/ / /1 2/1
Escort
1/ / /1 1/4
Miata
1/ / / /1
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24. Quantitative Analysis for Management
Miles/gallon
Normalized
Civic 34
.3010
Fuel Economy
(quantitative
information)
Saturn 27
.2390
Escort 24
.2120
Miata
Miata 28
113
.2480
1.0
Since we have quantitative information, it is not required to compare alternatives pair-wise.
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25. Quantitative Analysis for Management
- Civic
- Saturn .2470
- Escort .0600
- Miata
- Civic
- Saturn
- Escort
- Miata
- Civic
- Saturn
- Escort
- Miata
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26. Ranking of alternatives
Style Reliability Fuel
Economy
Civic
Escort
Miata
Saturn *
.3196
.5584
.1220 =
.3060
.2720
.0940
.3280
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27. Quantitative Analysis for Management
Complex decisions
Many levels of criteria and sub-criteria
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28. Quantitative Analysis for Management
Example
Level 1: Evaluation of Representatives
Level 2:
Commercial Evaluation
Service Evaluation
Management Evaluation
Technical Evaluation
Level 3 Attributes of Level 2
Level 4 Representatives
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29. Quantitative Analysis for Management
Level 3
Commercial Attributes
Amount of Spare parts Purchasing
Credit
Ratio of Returns to Purchasing
Ratio of Debits to Purchasing
Ratio of Purchasing to Forcast
Ratio of Purchasing to Guarantee
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30. Quantitative Analysis for Management
Level 3
Service Attributes
Initial Service
Guarantee
Repair
Management Attributes
Manpower
Systems
Communications
Management
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31. Quantitative Analysis for Management
Level 3
Technical Attributes
Building
Equipment
Tools
Security system
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32. Quantitative Analysis for Management
Consistency
In pair-wise comparison, if alternative A is preferred over B and B is preferred over C, then clearly A must be preferred over C. Now if in pair-wise comparison C is preferred over A, it is said that the system is not consistent.
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33. Quantitative Analysis for Management
Consistency Test
Step 1. Multiply the pair-wise comparison matrix by the average rating. The result is called weighted sum vector.
Step 2. Divide the vector of Step 1 by the average rating. The result is called consistency vector.
Step 3. is the sum of consistency vector elements.
Step 4. Calculate ,where n is the number of items.
Step 5. Determine RI, from table on page 526, for example for n=3, RI=0.58.
Step 6. Calculate CR= CI/RI. If CR <0.1, then it is consistent.
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34. AHP and Related Software
Expert Choice (Forman)
Criterium DecisionPlus (Hearne Scientific Software)
HIPRE 3+ (Systems Analysis Laboratory, Helsinki)
Web-HIPRE
Super Decisions (Saaty)
EC Resource Aligner combines optimization with AHP to select the optimal combination of alternatives or projects subject to a budgetary constraint
The first web-based multiattribute decision analysis tool
This software implements the analytic network process (decision making with dependence and feedback) 7

35. Quantitative Analysis for Management
Group Decision Making
Group Problem Solving Techniques
Brainstorming process to generate a quantity of ideas
Delphi Technique process to generate ideas from physically dispersed experts
Nominal Group Technique process to generate ideas and evaluate solutions
Computer-Aided Decision Making
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36. Quantitative Analysis for Management
Special topics in AHP
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37. Modeling Group Decisions
Suppose there are n decision makers
Most common approach
Have each decision maker k fill in a comparison matrix independently to obtain [ akij ]
Combine the individual judgments using the geometric mean to produce entries A = [ aij ] where
EM is applied to A to obtain the priority vector
aij = [ a1ij x a2ij x … x anij ] 1/n 38

38. Extending the 1-9 Scale to 1- 
The 1-9 AHP scale does not limit us if we know how to use clustering of similar objects in each group and use the largest element in a group as the smallest one in the next one. It serves as a pivot to connect the two.
We then compare the elements in each group on the 1-9 scale get the priorities, then divide by the weight of the pivot in that group and multiply by its weight from the previous group. We can then combine all the groups measurements as in the following example comparing a very small cherry tomato with a very large watermelon.

40. Clustering & Comparison
Color
How intensely more green is X than Y relative to its size?
Honeydew Unripe Grapefruit Unripe Cherry Tomato
Unripe Cherry Tomato Oblong Watermelon Small Green Tomato
Small Green Tomato Sugar Baby Watermelon Large Lime

41. Quantitative Analysis for Management
Application Areas
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42. Illustrative Problem: Best Site Selection
The ABC Restaurant Corporation is offering franchise opportunities. After completing all the requirements from the applicants, the company seeks the best site location from a set of alternative locations. There are three DMs to make the judgments: CEO, CFO, and CIO.

43. The Analytic Hierarchy Process
Illustrative example
Level 1: Focus
Best Fishery
Management Policy
Level 2: Criteria
Scientific
Economic
Political
Level 3:
Subcriteria
Statewide
Local
Level 4:
Alternatives
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Partial Hierarchy: Management of a Fishery