MODULE 1
Analytic Hierarchy Process
TEACHING SUGGESTIONS
Teaching Suggestion M1.1: Using Multifactor Decision-Making Techniques.
Many decisions students make involve a number of factors. Thus, multifactor decision-making
techniques can be useful and practical. This section can be started by having students give
Teaching Suggestion M1.2: Using AHP.
Have the students describe situations where AHP would be preferred over the multifactor
SOLUTIONS TO QUESTIONS AND PROBLEMS
M1-1. Multifactor decision making is appropriate when a decision involves a number of factors.
M1-2. When using multifactor decision making, each factor receives an importance weight.
These weights will sum to 1. Then every alternative and factor combination will receive a factor
evaluation for each alternative. The alternative with the highest weighted evaluation is selected.
M1-3. The analytic hierarchy process should be used when it is difficult or impossible to
M1-4. Here is an analysis of George’s decision.
Factor weights:
Factor
Importance (Weight)
Price
0.4
Color
0.1
Warranty
0.1
Size
0.1
Brand name
0.3
Factor evaluations:
Factor
Sun
Hitek
Surgo
Price
0.7
0.6
0.8
Color
0.9
0.9
0.4
Warranty
0.8
0.9
0.4
Size
0.8
0.8
0.2
Brand name
0.9
0.9
0.6
Evaluation of SUN:
Factor
Factor
Weighted
Rating
Evaluation
Evaluation
0.4
0.7
0.28
0.1
0.9
0.09
0.1
0.8
0.08
0.1
0.8
0.08
0.9
0.27
1.0
0.80
Evaluation of HITEK:
Factor
Factor
Factor
Weighted
Name
Rating
Evaluation
Evaluation
Price
0.4
0.6
0.24
Color
0.1
0.9
0.09
Warranty
0.1
0.9
0.09
Size
0.1
0.8
0.08
Brand name
0.9
0.27
1.0
0.77
Evaluation of SURGO:
Factor
Factor
Factor
Weighted
Name
Rating
Evaluation
Evaluation
Price
0.4
0.8
0.32
Color
0.1
0.4
0.04
Warranty
0.1
0.4
0.04
Size
0.1
0.2
0.02
Brand name
0.3
0.6
0.18
1.0
0.60
SUN is selected, with the highest total weighted evaluation of 0.80.
M1-5. Linda’s problem can be analyzed as follows:
Price
Car 1
Car 2
Car 3
Car 1
2
7
Car 2
4
Car 3
The following will be the priorities for price:
Priority for car 1 is 0.6025.
M1-6.
Warranty
Car 1
Car 2
Car 3
Car 1
1/3
1/8
Car 2
1/5
Car 3
The following will be the priorities for warranty:
Priority for car 1 is 0.0768.
Priority for car 2 is 0.1863.
M1-7.
Style
Car 1
Car 2
Car 3
Car 1
1/3
3
Car 2
8
Car 3
The following will be the priorities for style:
Priority for car 1 is 0.2364.
Value of CI = 0.0008
RI = 0.5800
CR = 0.0013
M1-8.
Factors
Price
Style
Price
9
Warranty
6
Style
The following will be the priorities for the factors:
Priority for price is 0.6049.
The following are the final rankings—Car 1 is selected.
Item
Ranking
Car 1
0.4045
Car 2
0.2946
Car 3
0.3008
M1-9. The weighted averages of these scores are shown in the table. Gina should choose
Univesity B.
Weighted
Cost
Reputation
Quality of life
Average
Weight
0.6
0.2
0.2
A
4
9
7
5.6
B
8
5
7
7.2
C
7
6
3
6.0
M1-10. Using AHP, we have the following matrices.
Cost
A
B
C
A
1
0.2
0.333333
B
5
C
3
0.333333
1
Column Total
9
1.533333
4.333333
Factor Evaluation
Normalized
A
B
C
(Row Average)
A
0.1111
0.1304
0.0769
0.1062
B
0.5556
0.6522
0.6923
0.6333
C
0.3333
0.2174
0.2308
0.2605
Reputation
A
B
C
A
1
7
5
B
0.142857
1
0.333333
C
0.2
1
Column Total
1.342857
6.333333
Factor Evaluation
Normalized
A
B
C
(Row Average)
A
0.7447
0.6364
0.7895
0.7235
B
0.1064
0.0909
0.0526
0.0833
C
0.1489
0.2727
0.1579
0.1932
Quality of Life
A
B
C
A
1
1
5
B
1
1
7
C
0.2
1
Column Total
2.2
13
Normalized
A
B
C
Factor Evaluation
(Row Average)
A
0.4545
0.4667
0.3846
0.4353
B
0.4545
0.4667
0.5385
0.4866
C
0.0909
0.0667
0.0769
0.0782
Factors
Cost
Reputation
Quality of life
Cost
1
3
7
Reputation
0.333333
1
2
Quality of life
0.142857
0.5
Column Total
1.47619
4.5
Quality
Factor
Evaluation
Normalized
Cost
Reputation
of life
(Row Average)
Cost
0.6774
0.6667
0.7000
0.6814
Quality of life
0.0968
0.1111
0.1000
0.1026
Using the factor weights, we find the following weighted averages for each university.
Cost
Reputation
Quality
Weighted
of life
Average
A
0.1062
0.7235
0.4353
0.2733
B
0.6333
0.0833
0.4866
0.4995
C
0.2605
0.1932
0.0782
0.2272
Weights
0.6814
0.2160
0.1026
M1-11. The analysis to determine which computer system is to be selected is as follows:
Price
S-1
S-2
S-3
S-1
2
8
S-2
5
S-3
The following will be the priorities for price:
Priority for system 1 (S-1) is 0.6039.
Priority for system 2 (S-2) is 0.3258.
CR = 0.0048
Brand Name
S-1
S-2
S-3
S-1
1
6
S-3
The following will be the priorities for brand name:
Priority for system 1 (S-1) is 0.4838.
Priority for system 2 (S-2) is 0.4232.
Priority for system 3 (S-3) is 0.0930.
Memory
S-1
S-2
S-3
S-1
1/2
1/7
S-2
S-3
The following will be the priorities for memory:
Priority for system 1 (S-1) is 0.0919.
RI = 0.5800
CR = 0.0281
Speed
S-1
S-2
S-3
S-1
1/3
2
S-2
5
S-3
The following will be the priorities for speed:
Priority for system 1 (S-1) is 0.2299.
RI = 0.5800
CR = 0.0032
Flexibility
S-1
S-2
S-3
S-1
1/2
1/8
S-2
1/4
S-3
The following will be the priorities for flexibility:
Priority for system 1 (S-1) is 0.0909.
RI = 0.5800
CR = 0.0000
PC
Compatibility
S-1
S-2
S-3
S-1
8
4
S-2
1/3
S-3
The following will be the priorities for PC compatibility:
Priority for system 1 (S-1) is 0.7146.
RI = 0.5800
CR = 0.0158
The following will be the weights for the factors:
Weight for price is 0.3849
Weight for brand name is 0.0447
Table for Factors for Problem M1-11
Brand
PC
Factors
Price
Name
Memory
Speed
Flexibility
Compatibility
Price
9
4
5
3
2
Brand name
1/2
1
1/4
1/5
Memory
2
1/2
1/6
Speed
1/3
1/6
Flexibility
1/2
compatible
Consistency information follows:
Lambda = 6.1441
Value of CI = 0.02 88
RI = 1.2400
CR = 0.0232
The following are the final rankings—system 1 (S-1) is selected.
Item
Ranking
System 1 (S-1)
0.4928
System 2 (S-2)
0.2400
System 3 (S-3)
0.2671