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Multiple-criteria decision-making

1

2

3

AHP (Analytical Hierarchy Process)

4

Car Selection Example
Car A \$13,100 18 Deluxe 4-door midsize AM/FM, tape 6-cylinder Car B \$11,200 23 Above av. 2-door sport AM/FM Car C \$9,500 29 Standard 2-door compact AM

Price MPG Interior Body Radio Engine

4-cylinder 4-cylinder turbo
5

Car Selection Example

Alternatives
Car A Car B Car C

Criteria
Price Miles per gallon (MPG) Comfort Style

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Hierarchy for the Car-Selection Problem
Overall Goal:
Select the best car

Criteria:

Price

MPG

Comfort

Style

Decision Alternatives:

Car A

Car B

Car C

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Pairwise Comparison Scale for AHP Preferences

Verbal Judgment of Preference
Extremely preferred Very strongly to extremely Very Strongly preferred Strongly to very strongly Strongly preferred Moderately to strongly Moderately preferred Equally to moderately Equally preferred

Numerical Rating
9 8 7 6 5 4 3 2 1
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Pairwise Comparison Matrix
Comfort Car A Car B Car C Car A Car B 2 Car C 8 6

aii = 1

aji =
Comfort Car A Car B Car C Car A 1 1/2 1/8 Car B 2 1 1/6 Car C 8 6 1

1

aij

9

Procedure for Synthesizing Judgments
Step 1. Sum the values in each column of pairwise comparison matrix (pcm) Step 2. Divide each element in the pcm by its column total; the resulting matrix is referred as the normalized pcm Step 3. Compute the average of the elements in each row of the normalized matrix; these averages provide an estimate of the relative priorities of the elements being compared.
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Example
Step 1
Comfort Car A Car B Car C
Column Totals

Car A 1 1/2 1/8 13/8

Car B 2 1 1/6 19/6

Car C 8 6 1 15

Step 2

Comfort Car A Car B Car C
Column Totals

Car A 8/13 4/13 1/13 1
Car B 0.632 0.316 0.053

Car B 12/19 6/19 1/19 1
Car C 0.533 0.400 0.067 Total

Car C 8/15 6/15 1/15 1
Row Ave.

Step 3

Comfort Car A Car B Car C

Car A 0.615 0.308 0.007

0.593

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