agenda for this week wednesday, april 27 ahp friday, april 29 ahp monday, may 2 exam 2
TRANSCRIPT
Agenda for This Week
Wednesday, April 27 AHP
Friday, April 29 AHP
Monday, May 2 Exam 2
Chapter 15
Analytical Hierarchy Process – Part 2
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
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 prioritiesRelative priorities
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
AHP - Steps
1. Make pairwise comparisons 2. Synthesize judgments 3. Check for consistency
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 wasn’t, some inconsistency would occur.
With AHP, we can measure the degree of consistency; and if unacceptable, we can revise pairwise comparisons
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 max) of the values from Step 2.
Step 4: Compute consistency index (CI) Step 5: Compute consistency ratio (CR)
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
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
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
Step 3: Compute average (denoted max) of the values from Step 2.
max = (3.019 + 2.988 + 3.075) / 3 = 3.027 = (3.019 + 2.988 + 3.075) / 3 = 3.027
Consistency – Step 3
Step 4: Compute consistency index (CI)
(where n = # items being compared)
CI = (max - n) / (n-1) = (3.027 - 3) / 2 =
.0135
This is called the Consistency Index
Consistency – Step 3
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 nValue of RI is based on n
n 3 4 5 6 7 8n 3 4 5 6 7 8
RI 0.58 0.90 1.12 1.24 1.32 1.41RI 0.58 0.90 1.12 1.24 1.32 1.41
Step 5: Compute consistency ratio (CR)
CR = CI / RI =
CR = .0135 / .58 = .023
Standard Rule states: If CR <= .10, consistency is acceptable!
Consistency – Step 3
AHP - Steps
1. Make pairwise comparisons 2. Synthesize judgments 3. Check for consistency
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
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