Agenda for This Week

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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 Process Part 2

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Step 2 - Synthesization
CRITERIA
Rent Size Prox
Rent 1 5 6
Size 1/5 1 1/3
Prox 1/6 3 1
SUM 41/30 9 22/3
Next divide each element by column total
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Step 2 - Synthesization
Relative priorities
CRITERIA
Rent Size Prox Avg
Rent .732 .556 .820 .702
Size .146 .111 .046 .101
Prox .122 .333 .136 .197
Normalized pairwise comparison matrix
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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
.702 .101 .197
Rent Size
Proximity Criteria
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AHP - Steps

• 1. Make pairwise comparisons ?
• 2. Synthesize judgments ?
• 3. Check for consistency

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AHP Step 3

• A key step in the making of several pairwise
  comparisons is considering the consistency of the
  pairwise judgements.
• Example If A compared to B 3 and B compared
  to C 2 then A compared to C should 3x2 6.
  If it wasnt, some inconsistency would occur.
• With AHP, we can measure the degree of
  consistency and if unacceptable, we can revise
  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
4 1 7
1 1/4 3
1/3 1/7 1
.266 .08 .654

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Consistency Step 3
Step 1 Multiply pairwise comparison matrix
(for rent) by relative priorities
.32 .08 .56
.265 .066 .795
.215 .093 .653
.80 .239 2.008

Weighted Sum Vector
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Consistency Step 3

• 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

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Consistency Step 3

• Step 3 Compute average (denoted lmax) of the
  values from Step 2.
• lmax (3.019 2.988 3.075) / 3 3.027

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Consistency Step 3

• 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

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Consistency Step 3

• Step 5 Compute consistency ratio (CR)
• CR CI / RI
• RI random index (CI of randomly generated
  pairwise comparison matrix)

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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Consistency Step 3

• Step 5 Compute consistency ratio (CR)
• CR CI / RI
• CR .0135 / .58 .023
• Standard Rule states If CR lt .10, consistency
  is acceptable!

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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
.702 .101 .197
Rent Size
Proximity Criteria
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Final Step

• 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

Rent
Size
Proximity