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 99258chen@gonzaga.edu

BUSINESS PERFORMANCE MANAGEMENT

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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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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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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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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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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

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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/

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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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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.

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A pairwise comparison matrix for the criteria level

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4251

NearnessInterestQualitySalary

NearnessInterestQualitySalarySatisfaction with a Job

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

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

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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.

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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

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12714

7/14/112/14

CJobBJobAJob

CJobBJobAJobNearness

A

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

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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

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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

NearnessInterestQualitySalary

NearnessInterestQualitySalarySatisfaction with a Job

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We will open an existing model

http://hipre.aalto.fi

File name: Mbus626_chen.jmdmbus673.jmd

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

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Scroll down

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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

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(p.4 of Handout)

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Result from double clicking “salary”

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Result from double clicking “life quality”

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Result from double clicking “interest”

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Result from double clicking “nearness to family”

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clickPerform Analysis

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Perform Analysis

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Result from “Analysis of Composite Priorities … “

click

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

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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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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)

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Your Turn …

How to create an AHP model for “a Job

Selection” Project

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We will open an existing model

http://hipre.aalto.fi

File name: Mbus626_chen.jmdmbus673.jmd

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You will learn how to create an AHP model for “a Job Selection” listed below

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Double click a node (element) will appear

Enter a nameGoal level

Criteria level

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Edit the element’s Name (only if needed)

Select this

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Steps of creating “Links”

1. Left click

2. Right click

Complete the remaining links

The “Goal” and “Alternative” displayed on their “Level” respectively

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Steps of creating “Links” (cont.)

1. Left click2. Right click

Complete the remaining links between “Criteria” and Alternatives”

Labels are changed

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

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

Enter “filename”

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Enter “filename”

A “filename” is saved

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Steps of assigning weights to different decision factors

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

and nearness to family)

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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

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Steps of assigning weights to different decision factors (cont.)Drag the bar or enter a number or click the bar to the “More Important” side

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

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

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

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

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

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

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

Click OK when done

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

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Double left click

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

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

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

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

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Perform Analysis

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Result from “Analysis of Composite Priorities … “

click

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

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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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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)

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Save your work again

click

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We will open an existing model

http://hipre.aalto.fi

File name: Mbus626_chen.jmdmbus673.jmd

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Add AHP software site toJava Site List

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Step 1: Click on Windows ( ) and then select “Control Panel”

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Step 2: Click “Security” and Add the site (http://hipre.aalto.fi) on the Java site list

See detailed instruction on the following slides

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Step 3: Work on “Control Panel”

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Step 4: Click on “Edit Site List” and then Select “Add”

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Step 5: Enter http://hipre.aalto.fi inside box of … Location and then click on “OK”

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Step 5: Click “Continue” on the Security Warning Menu

Step 6: Complete the processa. You will see now that the AHP software site list (i.e., http://hipre.aalto.hi) has been added to “Exception Site List” b. Click “OK” to exit the “Security” option and Exit the “Java Control Panel”c. Re-activate the Firefox browser and enter the URL http://hipre.aalto.fi

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End of Lecture