201502271602246 ANALYTICAL HIERARCHY PROCESS.ppt

1 1© 2003 Thomson© 2003 Thomson/South-Western/South-Western Slide Slide

The Analytical Hierarchy Process (AHP)The Analytical Hierarchy Process (AHP)

Developed by Thomas SaathyDeveloped by Thomas Saathy A method to select the best one A method to select the best one To answer the question “which one”?To answer the question “which one”?

•To buy a house from several To buy a house from several houseshouses

•To select a university from a group To select a university from a group of universitiesof universities

•To choose the most qualified To choose the most qualified candidate, etc.candidate, etc.


The Analytical Hierarchy Process The Analytical Hierarchy Process (AHP)(AHP)

AHP is a method to generate a AHP is a method to generate a numerical score to rank each numerical score to rank each decision alternativesdecision alternatives

The numerical score can be The numerical score can be calculated manually or can use calculated manually or can use excelexcel


The decision maker decides the The decision maker decides the “score” for each alternative on a “score” for each alternative on a criterion using pairwise criterion using pairwise comparison.comparison.


In pairwise comparison, the In pairwise comparison, the decision maker compares two decision maker compares two alternatives alternatives (a pair) according to one criterion (a pair) according to one criterion and indicates a preference. and indicates a preference.


Preference Scale for Piecewise ComparisonPreference Scale for Piecewise ComparisonPreference Level Numerical value

Equally Preferred 1

Equally to moderately Preferred

2

Moderately Preferred 3

Moderately to Strongly Preferred

4

Strongly Preferred 5

Strongly to very Strongly Preferred

6

Very Strongly Preferred 7

Very Strongly to Extremely Preferred

8

Extremely Preferred 9


Let illustrate AHP by using an example.Let illustrate AHP by using an example.

Suppose that PETRONAS has identified Suppose that PETRONAS has identified three potential sites for its latest project three potential sites for its latest project near Alor Setar (A), Bukit Merah (B) and near Alor Setar (A), Bukit Merah (B) and Cyberjaya (C). The company has identified Cyberjaya (C). The company has identified four primary criteria on which it will four primary criteria on which it will compare the sites namely:compare the sites namely:

PETRONAS SITE SELECTION PROBLEMPETRONAS SITE SELECTION PROBLEM


The customer market (overall market size, and The customer market (overall market size, and population at different age level)population at different age level)

Income levelIncome level Infrastructure (including utilities, and roads)Infrastructure (including utilities, and roads) Transportation (proximity to highway for supplier Transportation (proximity to highway for supplier

deliveries and customer access)deliveries and customer access)

The overall objective of the company is to The overall objective of the company is to select the best siteselect the best site

The four criteria:The four criteria:


1. Comparison matrix for customer market:1. Comparison matrix for customer market:

CUSTOMER MARKET

A B C

A 1 3 2

B 1/3 1 1/5

C 1/2 5 1


2. Comparison matrix for income level:2. Comparison matrix for income level:

INCOME LEVEL

A B C

A 1 6 1/3

B 1/6 1 1/9

C 3 9 1


3. Comparison matrix for infrastructure:3. Comparison matrix for infrastructure:

INFRASTRUCTURE

A B C

A 1 1/3 1

B 3 1 7

C 1 1/7 1


4. Comparison matrix for transportation:4. Comparison matrix for transportation:

TRANSPORTATION

A B C

A 1 1/3 1/2

B 3 1 4

C 2 1/4 1


Let us do Let us do synthesizationsynthesization: decision : decision alternatives are prioritized within each alternatives are prioritized within each

criterion.criterion.STEP 1STEP 1 CUSTOMER MARKET

A B C

A 1 3 2

B 1/3 1 1/5

C 1/2 5 1

Total 11/6 9 16/5


Next, we divide each value in a column by its Next, we divide each value in a column by its corresponding column sum. This results in a corresponding column sum. This results in a normalized matrix as follows:normalized matrix as follows:

STEP 2STEP 2 CUSTOMER MARKET

A B C

A 6/11 3/9 5/8

B 2/11 1/9 1/16

C 3/11 5/9 5/16


Next, change them to decimal and find the Next, change them to decimal and find the average for each row.average for each row.

STEP 3 CUSTOMER MARKETCUSTOMER MARKET

A B C Rowaverage

A 0.5455 0.3333 0.6250 0.5012

B 0.1818 0.1111 0.0625 0.1185

C 0.2727 0.5556 0.3125 0.3803


Thus, based on Thus, based on customer marketcustomer market, the sites , the sites are ranked as follows:are ranked as follows:

0.5012 (A)

0.1185 (B)

0.3803 (C)

OROR

0.5012 (A)

0.3803 (C)

0.1185 (B)


We have to do the same process to the We have to do the same process to the other 3 criteria. The results are as follows:other 3 criteria. The results are as follows:

Income Level

0.2819 (A)

0.0598 (B)

0.6583 (C)

Infrastructure

0.1780 (A)

0.6850 (B)

0.1360 (C)

Transportation

0.1561 (A)

0.6196 (B)

0.2243 (C)


CRITERIA (CALL THIS MATRIX M)

MARKET INCOME LEVEL

INFRA-STRUCTURE

TRANSPORTATION

A 0.5012 0.2819 0.1790 0.1561

B 0.1185 0.0598 0.6850 0.6196

C 0.3803 0.6583 0.1360 0.2243

LET COMBINE ALL 4 CRITERIA TOGETHER.LET COMBINE ALL 4 CRITERIA TOGETHER.


NEXT, WE WANT TO RANK THE CRITERIA.NEXT, WE WANT TO RANK THE CRITERIA.


CM IL IS TP

CM 1 1/5 3 4

IL 5 1 9 7

IS 1/3 1/9 1 2

TP 1/4 1/7 1/2 1

WE’LL ASK THE DM TO FILL THIS TABLE.WE’LL ASK THE DM TO FILL THIS TABLE.


WE’LL DO THE SAME PROCESS AS BEFORE: WE’LL DO THE SAME PROCESS AS BEFORE: NOW, ADD THE VALUES IN EACH COLUMNNOW, ADD THE VALUES IN EACH COLUMN

CM IL IS TP

CM 1 1/5 3 4

IL 5 1 9 7

IS 1/3 1/9 1 2

TP 1/4 1/7 1/2 1

TOT 79/1279/12 458/315458/315 27/227/2 1414


NEXT, DIVIDE EACH ENTRY WITH RESPECTIVE NEXT, DIVIDE EACH ENTRY WITH RESPECTIVE COLUMN SUM.COLUMN SUM.

CM IL IS TP

CM 12/79 315/2290 6/27 4/14

IL 18/27 7/14

IS 2/27 2/14

TP 1/27 1/14


NEXT, WRITE EACH ENTRY INTO DECIMAL FORM.NEXT, WRITE EACH ENTRY INTO DECIMAL FORM.

CM IL IS TP

CM 0.1519 0.1375 0.2222 0.2857

IL 0.6667 0.5000

IS 0.0741 0.1429

TP 0.0370 0.0714


CM IL IS TP Average Row

CM 0.1519 0.1375 0.2222 0.2857 0.19930.1993

IL 0.6667 0.5000

IS 0.0741 0.1429

TP 0.0370 0.0714

NEXT, TAKE AVERAGE FOR EACH ROW. NEXT, TAKE AVERAGE FOR EACH ROW.


THOSE NUMBERS REFLECT THE RANK FOR THE THOSE NUMBERS REFLECT THE RANK FOR THE CRITERIA. WE ARE SUPPOSE TO HAVE:CRITERIA. WE ARE SUPPOSE TO HAVE:

ROW AVERAGES (CALL THIS MATRIX N)

0.1993 (CM)

0.6535 (IL)

0.0860 (IS)

0.0612(TP)


0612.0

0860.0

6535.0

1993.0

2243.01360.06583.03803.0

6196.06850.00598.01185.0

1561.01790.02819.05012.0

NOW WE ARE READY TO DEVELOP AN OVERALL NOW WE ARE READY TO DEVELOP AN OVERALL RANKING. WHAT WE HAVE TO DO IS TO MULTIPLY RANKING. WHAT WE HAVE TO DO IS TO MULTIPLY MATRIX M AND N. MATRIX M AND N.


WE ARE SUPPOSE TO GET:WE ARE SUPPOSE TO GET:

5314.0

1595.0

3091.0Score for site A

Score for site B

Score for site C


SCORE FOR SITE C IS 0.5314 SCORE FOR SITE C IS 0.5314 SCORE FOR SITE A IS 0.3091SCORE FOR SITE A IS 0.3091SCORE FOR SITE B IS 0.1595SCORE FOR SITE B IS 0.1595

THUS, SITE C (CYBERJAYA) IS THE BEST CHOICE.THUS, SITE C (CYBERJAYA) IS THE BEST CHOICE.

REARRANGE ACCORDING TO SCORE:REARRANGE ACCORDING TO SCORE:


Make your own summary of Make your own summary of stepssteps


Assignment: Use excel to solve Assignment: Use excel to solve “Petronas Site Selection “Petronas Site Selection

Problem”.Problem”.


Food of thought…

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization.

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201502271602246 ANALYTICAL HIERARCHY PROCESS.ppt