analytical hierarchy process (ahp): a multi-objective decision making technique

AHP - 1Dr. Chen – Business Intelligence

Analytical Hierarchy Process (AHP): A Multi-Objective Decision

Making Technique

Jason C.H. Chen, Ph.D.Professor of MIS

School of BusinessGonzaga UniversitySpokane, WA 99258

[email protected]

BUSINESS PERFORMANCE MANAGEMENT


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.


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.


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


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.


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.


Satisfaction with a Job

Job A Job B Job C

Structure of the Problem

Starting Salary Life Quality Interest Nearness to

Family

criteria; n=4


Satisfaction with a Job

Starting Salary Life Quality Interest Nearness to

Family

Job A Job B Job C

Structure of the Problem

Web site:http://www.hipre.hut.fi/

criteria; n=4


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


A pairwise comparison matrix for the criteria level

12/124/12122/12/12/115/1

4251

NearnessInterestQualitySalary

NearnessInterestQualitySalarySatisfaction with a Job

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.


A pairwise comparison matrix for the criteria level

12/124/12122/12/12/115/1

4251



Web site:http://www.hipre.hut.fi/

Since n=4, there are 6 [n*(n-1)/2] judgments required to develop each matrix. Why?


12/14/1212/1421

1

CJobBJobAJob

CJobBJobAJobSALARY

A

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.


1333/1123/12/11

2

CJobBJobAJob

CJobBJobAJobQuality

A

The next two pairwise matrices (for “Life Quality” and “Interest”) are as follows (see step#6 on the handout):

13/133173/17/11

3

CJobBJobAJob

CJobBJobAJobInterest

A


12714

7/14/112/14

CJobBJobAJob

CJobBJobAJobNearness

A

The last pairwise matrix (for “Nearness to family”) is listed below:


0159.03

40477.41

.. max

n

nIC

Consistency Index (C.I) is computed as follows (see handout, p.5)

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:

How to verify that the data entered in the comparison matrices is acceptable

C.R. = C.I. / R.I. = 0.0159/0.9 = 0.0176666 = 1.7% < 10%

n 2 3 4 5 6 7 8 9 10R.I. 0 .58 .90 1.12 1.24 1.32 1.41 1.45 1.51

Random Indices (R.I.) for Consistency Check


12/14/1212/1421

1

CJobBJobAJob

CJobBJobAJobSALARY

A

1333/1123/12/11

2

CJobBJobAJob

CJobBJobAJobQuality

A

13/133173/17/11

3

CJobBJobAJob

CJobBJobAJobInterest

A

12714

7/14/112/14

CJobBJobAJob

CJobBJobAJobNearness

A

12/124/12122/12/12/115/1

4251




We will open an existing model

http://hipre.aalto.fi

File name: Mbus626_chen.jmdmbus673.jmd


JAVA update (might be needed)The site list to add should be: http://hipre.aalto.fi/

http://hipre.aalto.fi/


double clickDouble

click

Display the “weights” entered in the “Goal” or “Criteria”1) Double click or 2) Select an “Element” then click Priorities then AHP


(p.4 of Handout)


Result from “Analysis of Composite Priorities … “

click

According to the BAR chart, AHP suggests that Jane should take Job B


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)


Result as Text Value Tree0 satisfaction with a job 1 salary 0.512 2 job A 0.571 2 job B 0.286 2 job C 0.143 1 life quality 0.098 2 job A 0.163 2 job B 0.540 2 job C 0.297 1 interest 0.244 2 job A 0.088 2 job B 0.669 2 job C 0.243 1 nearness to family 0.146 2 job A 0.082 2 job B 0.315 2 job C 0.603 Composite Priorities job A job B job C salary 0.293 0.146 0.073 life quali 0.016 0.053 0.029 interest 0.021 0.163 0.059 nearness t 0.012 0.046 0.088 Overall 0.342 0.408 0.249

1429.02857.05714.0

1S

2971.05409.01633.0

2S

2431.06687.00882.0

3S

6025.03151.00824.0

4S

step 7 (p.5)


Save your work again

click

analytical hierarchy process (ahp): a multi-objective decision making technique

Documents

salary row

criterion salary

criteria level satisfaction

comparison matrix

objective satisfaction

problemwhat job offer

quality column

following criteria objectives