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Agenda for This Week

Wednesday, April 27 AHP

Friday, April 29 AHP

Monday, May 2 Exam 2

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Chapter 15

Analytical Hierarchy ProcessPart 2

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Step 2 - Synthesization

CRITERIA

Next divide each element by column total

Rent Size Prox

Rent 1 5 6

Size 1/5 1 1/3

Prox 1/6 3 1

SUM 41/30 9 22/3

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Step 2 - Synthesization

Rent Size Prox Avg

Rent .732 .556 .820 .702

Size .146 .111 .046 .101

Prox .122 .333 .136 .197

CRITERIA

Normalized pairwise comparison matrix

Relative priorities

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Summary - Synthesization

Summary of Relative Priorities for

Rent, Size, Proximity and Criteria

.266

.080

.654

.125

.750

.125

.737

.186

.077

Rent Size Proximity Criteria

.702

.101

.197

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AHP Step 3

A key step in the making of several pairwisecomparisons is considering the consistencyof the pairwise judgements.

Example: If A compared to B = 3 and Bcompared to C = 2 then A compared to C should= 3x2 = 6. If it wasnt, some inconsistency wouldoccur.

With AHP, we can measure the degree ofconsistency; and if unacceptable, we canrevise pairwise comparisons

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Consistency Step 3

Step 1: Multiply pairwise comparison matrix

by relative priorities

Step 2: Divide weighted sum vector

elements by associated priority value

Step 3: Compute average (denoted lmax) of

the values from Step 2.

Step 4: Compute consistency index (CI)

Step 5: Compute consistency ratio (CR)

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Consistency Step 3

Step 1: Multiply pairwise comparison matrix

(for rent) by relative priorities

.266 + .08 + .654 =

1

1/4

3

4

1

7

1/3

1/7

1

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Consistency Step 3

Step 1: Multiply pairwise comparison matrix

(for rent) by relative priorities

.265

.066

.795

.32

.08

.56

.215

.093

.653

+ + =

.80

.239

2.008

Weighted Sum Vector

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Step 2: Divide weighted sum vector

elements by associated relative priority value

.80/.266 = 3.019

.239/.08 = 2.988

2.008/.654 = 3.075

Consistency Step 3

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Step 3: Compute average (denoted lmax) of

the values from Step 2.

lmax = (3.019 + 2.988 + 3.075) / 3 = 3.027

Consistency Step 3

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Step 4: Compute consistency index (CI)

(where n = # items being compared)

CI = (lmax - n) / (n-1) = (3.027 - 3) / 2 =

.0135

This is called the Consistency Index

Consistency Step 3

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Step 5: Compute consistency ratio (CR)

CR = CI / RI

RI = random index (CI of randomly generated

pairwise comparison matrix)

Consistency Step 3

Value of RI is based on n

n 3 4 5 6 7 8

RI 0.58 0.90 1.12 1.24 1.32 1.41

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Step 5: Compute consistency ratio (CR)

CR = CI / RI =

CR = .0135 / .58 = .023

Standard Rule states: If CR

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AHP - Steps

1. Make pairwise comparisons

2. Synthesize judgments

3. Check for consistency

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Summary - Synthesization

Summary of Relative Priorities for

Rent, Size, Proximity and Criteria

.266

.080

.654

.125

.750

.125

.737

.186

.077

Rent Size Proximity Criteria

.702

.101

.197

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Develop Overall Priority Ranking

Overall Apartment 1 Priority

.702(.266) + .101(.125) + .197(.737) = .344

Overall Apartment 2 Priority

.702(.08) + .101(.75) + .197(.186) = .169

Overall Apartment 3 Priority

.702(.653) + .101(.125) + .197(.076) = .486

Final Step

Rent Size Proximity