BUSINESS PERFORMANCE MANAGEMENT
Analytical Hierarchy Process
(AHP): A Multi-Objective
Decision Making Technique
Jason C.H. Chen, Ph.D.
Professor of MIS
School of Business
Gonzaga University
Spokane, WA 99258
chen@jepson.gonzaga.edu
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AHP - 1
Analytical Hierarchy Process
• In many situations one may not be able to
assign weights to the different decision
factors. Therefore one must rely on a
technique that will allow the estimation of the
weights.
• What is a solution?
• One such process, The Analytical Hierarchy
Process (AHP), involves pairwise
comparisons between the various factors.
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AHP - 2
Analytical Hierarchy Process (cont.)
• The process is started by the decision
maker creating the value tree associated
with the problem.
• Then proceed by carrying out pairwise
comparisons, both between
– Alternatives on each factor, and
– Factors at a given node.
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AHP - 3
Application Case of AHP
•
Jane is about to graduate from college and
is trying to determine which job offer to
accept. She plans to choose between three
offers by determining how well each offer
meets the following criteria (objectives):
–
–
–
–
High starting salary
Quality of life in city where job is located
Interest of work
Nearness of job to family
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AHP - 4
Assumptions
• Jane has hard time in prioritizing those
criteria. In other words, she needs to
find one way to decide the weights for
those criteria. AHP provides such a
function.
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Determine the problem
• What job offer will give Jane possibly
highest satisfaction?
• Structure the hierarchy by putting the top
objective (satisfaction with job), criteria,
and alternatives as follows.
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AHP - 6
Structure of the Problem
Satisfaction
with a Job
criteria;
n=4
Starting
Salary
Job A
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Life Quality
Job B
Interest
Nearness to
Family
Job C
AHP - 7
Structure of the Problem
Satisfaction
with a Job
criteria;
n=4
Starting
Salary
Job A
Life Quality
Job B
Web site:
http://www.hipre.hut.fi/
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Interest
Nearness to
Family
Job C
AHP - 8
The Principle of the AHP …
• The principle of the AHP relies on the pairwise
comparison. This comparison is carried out using a
scale from 1 to 9 as follows:
–
–
–
–
–
–
–
–
–
1 Equally preferred
2 Equally to Moderately preferred
3 Moderately preferred
4 Moderately to Strongly preferred
5 Strongly preferred
6 Strongly to Very Strongly preferred
7 Very Strongly preferred
8 Very to Extremely Strongly preferred
9 Extremely preferred
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AHP - 9
A pairwise comparison matrix for the criteria level
Satisfaction
with a Job
Salary
Quality
Interest
Nearness
Salary
1
5
2
4
Quality
1/5
1
1/ 2
1/ 2
Interest
1/ 2
2
1
2
Nearness
1/ 4
2
1/ 2
1
 We assume that “Starting Salary” is strongly more important than “Life
Quality”. That is why 5 is entered into the Salary row and Quality
column.
 Compared to Interest, Salary is just a little bit more important. That is
why 2 is entered into Salary row and Quality column.
 Similarly, Salary is moderately to strongly preferred than “Nearness”.
That is why 4 is entered into the Salary row and Nearness column.
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AHP - 10
A pairwise comparison matrix for
the criteria level
Satisfaction
with a Job
Salary
Quality
Interest
Nearness
Salary
1
5
2
4
Quality
1/5
1
1/ 2
1/ 2
Interest
1/ 2
2
1
2
Nearness
1/ 4
2
1/ 2
1
Web site:
http://www.hipre.hut.fi/
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Since n=4, there are 6
[n*(n-1)/2] judgments
required to develop
each matrix. Why?
AHP - 11
Using the same steps of 3 and 4 (see handout) to
determine the score of each alternative on each
criterion. Take the first criterion “Salary” as an
example. One pairwise matrix is constructed as
follows (details see step 4 on the handout):
In terms of criterion of “Salary”, Job A is moderately
important (“2”) than Job B. However, Job A is essentially
more important (“4”) than Job C.
SALARY
A1 
Job A
Job B
Job C
Job A
1
2
4
Job B
1/ 2
1
2
Job C
1/ 4
1/ 2
1
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AHP - 12
The next two pairwise matrices (for “Life Quality” and
“Interest”) are as follows (see step#6 on the handout):
Quality
A2 
A3 
Job A
Job B
Job C
Job A
1
1/ 2
1/3
Job B
2
1
1/3
Job C
3
3
1
Interest
Job A
Job B
Job C
Job A
1
1/ 7
1/ 3
Job B
7
1
3
Job C
3
1/ 3
1
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AHP - 13
The last pairwise matrix (for “Nearness to family”)
is listed below:
A4 
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Nearness
Job A
Job B
Job C
Job A
1
1/ 4
1/ 7
Job B
4
1
1/ 2
Job C
7
2
1
AHP - 14
How to verify that the data entered in the comparison
matrices is acceptable
Consistency Index (C.I) is computed as follows (see handout, p.5)
C .I . 
 max  n
n 1

4 . 0477  4
 0 . 0159
3
We then compare the value of C.I. to the value of random index
(R.I). If the ratio of C.I. to R.I. is less than 10%, then we can say
the judgment process is relatively consistent and the matrix is
acceptable. Otherwise, the decision maker may need to re-examine
the judgment process and re-compare criteria or alternatives. The
consistency ratio (C.R.) is computed as follows:
C.R. = C.I. / R.I. = 0.0159/0.9 = 0.0176666 = 1.7% < 10%
Random Indices (R.I.) for Consistency Check
n
R.I.
2
0
3
.58
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4
.90
5
1.12
6
1.24
7
1.32
8
1.41
9
1.45
10
1.51
AHP - 15
Satisfaction with a
Job
Quality
Interest
Nearness
Salary
1
5
2
4
Quality
1/5
1
1/ 2
1/ 2
Interest
1/ 2
2
1
2
Nearness
1/ 4
2
1/ 2
1
SALARY
A1 
Salary
Job A
Job B
Job C
Job A
1
2
4
Job B
1/ 2
1
2
Job C
1/ 4
1/ 2
1
A3 
Interest
Job A
Job B
Job C
Job A
1
1/ 7
1/ 3
Job B
7
1
3
Job C
3
1/ 3
1
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A2 
A4 
Quality
Job A
Job B
Job C
Job A
1
1/ 2
1/3
Job B
2
1
1/3
Job C
3
3
1
Nearness
Job A
Job B
Job C
Job A
1
1/ 4
1/ 7
Job B
4
1
1/ 2
Job C
7
2
1
AHP - 16
We will open an existing model
http://www.hipre.hut.fi
or
http://hipre.aalto.fi/
File name:
mbus673.jmd
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AHP - 17
Display the “weights” entered in the “Goal” or “Criteria”
1) Double click or 2) Select an “Element” then click Priorities then AHP
Double
click
double
click
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AHP - 18
(p.4 of Handout)
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AHP - 19
Result from “Analysis of Composite Priorities … “
click
According to the BAR chart, AHP suggests that Jane should take Job B
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AHP - 20
Result from “Analysis of Composite Priorities … “ – with Values
According to the “Values”, AHP suggests that Jane should take Job B (you need to
“Add total” , see the next slide)
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AHP - 21
Result as Text
Value Tree
0 satisfaction with a job
1 salary 0.512
 0 . 5714 
2 job A 0.571
S 1   0 . 2857 
2 job B 0.286


0
.
1429


2 job C 0.143

1 life quality 0.098
 0 . 1633 
2 job A 0.163
S 2   0 . 5409 
2 job B 0.540


2 job C 0.297
0
.
2971


1 interest 0.244
 0 . 0882 


2 job A 0.088
S 3  0 . 6687


2 job B 0.669
 0 . 2431 
2 job C 0.243
1 nearness to family 0.146
2 job A 0.082
 0 . 0824 


2 job B 0.315
S 4  0 . 3151


2 job C 0.603
 0 . 6025 

Composite Priorities
job A
salary
0.293
life quali 0.016
interest
0.021
nearness t 0.012
Overall
0.342
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job B
0.146
0.053
0.163
0.046
0.408
step 7 (p.5)

job C
0.073
0.029
0.059
0.088
0.249
AHP - 22
Save your work again
click
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AHP - 23