AHP - 1 Dr. Chen – Business Intelligence Analytical Hierarchy Process (AHP): A Multi-Objective...

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 InterestNearness to

Family

criteria; n=4


Satisfaction with a Job

Starting Salary

Life Quality InterestNearness to

Family

Job A Job B Job C

Structure of the Problem

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


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

12/124/1

2122/1

2/12/115/1

4251

Nearness

Interest

Quality

Salary

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

12/124/1

2122/1

2/12/115/1

4251

Nearness

Interest

Quality

Salary


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

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


12/14/1

212/1

4211

CJob

BJob

AJob

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.


133

3/112

3/12/112

CJob

BJob

AJob

CJobBJobAJobQuality

A

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

13/13

317

3/17/113

CJob

BJob

AJob

CJobBJobAJobInterest

A


127

14

7/14/11

2/14

CJob

BJob

AJob

CJobBJobAJobNearness

A

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


0159.03

40477.4

1.. 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


12/14/1

212/1

4211

CJob

BJob

AJob

CJobBJobAJobSALARY

A

133

3/112

3/12/112

CJob

BJob

AJob

CJobBJobAJobQuality

A

13/13

317

3/17/113

CJob

BJob

AJob

CJobBJobAJobInterest

A

127

14

7/14/11

2/14

CJob

BJob

AJob

CJobBJobAJobNearness

A

12/124/1

2122/1

2/12/115/1

4251

Nearness

Interest

Quality

Salary



We will open an existing model

http://www.hipre.hut.fi

or

http://hipre.aalto.fi/

File name: mbus673.jmd

http://hipre.aalto.fi/


Scroll down


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 double clicking “salary”


Result from double clicking “life quality”


Result from double clicking “interest”


Result from double clicking “nearness to family”


click

Perform Analysis


Perform Analysis


Result from “Analysis of Composite Priorities … “

click

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


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

1429.0

2857.0

5714.0

1S

2971.0

5409.0

1633.0

2S

2431.0

6687.0

0882.0

3S

6025.0

3151.0

0824.0

4S

step 7 (p.5)


Your Turn -- Try It!



How to create an AHP model for “a Job Selection.”


Double click a node (element) will appear

Enter a nameGoal level

Criteria level


Edit the element’s Name (only if needed)

Select this


Steps of creating “Links”

1. Left click

2. Right click

Complete the remaining links


Steps of creating “Links” (cont.)

1. Left click2. Right click

Complete the remaining links between “Criteria” and Alternatives”

Labels are changed


Steps of creating “Links” – Final Model (cont.) Labels are changed


Be sure that to save the model now (and periodically).

Enter “filename”


Enter “filename”

A “filename” is saved


Steps of assigning weights to different decision factors

• Goal level (satisfaction with job)• Criteria level (salary, life quality, interest,

and nearness to family)


Double Left click

Steps of assigning weights to different decision factors

Click on “AHP”

We will first enter “pairwise comparison matrix” for the

“Criteria” level


Steps of assigning weights to different decision factors (cont.)

Drag the bar or enter a number

“Starting Salary” is strongly more important than “Life Quality”. That is why 5 is entered into the Salary row and Quality column.



Click OK when done

This completes “pairwise comparison matrix” for the “Goal” level (i.e., “Satisfaction with a Job”)


Double left click


Next, to complete “pairwise comparison matrix” for the “Criteria” level of “Salary”)


Perform Analysis


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

1429.0

2857.0

5714.0

1S

2971.0

5409.0

1633.0

2S

2431.0

6687.0

0882.0

3S

6025.0

3151.0

0824.0

4S

step 7 (p.5)


Save your work again

click


Have a fun!


File name: mbus673.jmd


• The following slides might be skipped.


Sensitivity Analysis

AHP - 1 Dr. Chen – Business Intelligence Analytical Hierarchy Process (AHP): A Multi-Objective...

Documents

Transcript of AHP - 1 Dr. Chen – Business Intelligence Analytical Hierarchy Process (AHP): A Multi-Objective...