Transcript Chapter 13

Agenda for This Week
Monday, April 25
AHP
Wednesday, April 27
AHP
Friday, April 29
AHP
Monday, May 2
Exam
2
Chapter 15
Analytical Hierarchy Process –
Part 1
Analytical Hierarchy Process
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Designed to solve multicriteria decision
problems
Model under conditions of certainty where we
know all of the info but we need to trade-off
many factors.
We are comparing several alternatives on the
basis of the same set of attributes.
Developing the Hierarchy
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Develop a visual representation of the
problem in terms of the overall goal, the
criteria to be used and the decision
alternatives
GOAL
Attributes
Alternatives
AHP Example
Decision Hierarchy
Select Best Apartment
Criteria
Alternatives
Rent
Size
Proximity
Apt. 1
Apt. 1
Apt. 1
Apt. 2
Apt. 2
Apt. 2
Apt. 3
Apt. 3
Apt. 3
AHP
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Major question is how to assign relative
weights across alternatives, as well as for the
attributes (assigning weights is the crux of
AHP).
People have been found to be more
consistent when they do pairwise
comparisons than when they just try to assign
relative weights.
AHP - Steps
1. Make pairwise comparisons
2. Synthesize judgments
3. Check for consistency
AHP – Pairwise Comparison
Scale (Always Use)
Verbal Judgement of Preferences
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
Step 1 – Pairwise Comparison
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Make pairwise comparison for CRITERIA
CRITERIA
Rent
Size
Proximity
Rent
1
5
6
Size
1/5
1
1/3
Proximity
1/6
3
1
Step 1 – Pairwise Comparison

Make pairwise comparison for each attribute
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Apt 1 compared to Apt 2
Apt 2 compared to Apt 3
Apt 1 compared to Apt 3
For RENT
Step 1 – Pairwise Comparison
RENT
Apt 1
Apt 2
Apt 3
Apt 1
1
4
1/3
Apt 2
¼
1
1/7
Apt 3
3
7
1
Step 1 – Pairwise Comparison
SIZE
Apt 1
Apt 2
Apt 3
Apt 1
1
1/6
1
Apt 2
6
1
6
Apt 3
1
1/6
1
Step 1 – Pairwise Comparison
PROXIMITY
Apt 1
Apt 2
Apt 3
Apt 1
1
5
8
Apt 2
1/5
1
3
Apt 3
1/8
1/3
1
AHP - Steps
1. Make pairwise comparisons
2. Synthesize judgments
3. Check for consistency
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AHP – Step 2
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Synthesization – the process of calculating
the priority of each criterion in terms of its
contribution to the overall goal of achieving
your goal
Step 2 - Synthesization
Step 1: Sum values in each column of
pairwise comparison matrix
Step 2: Divide each element by its column
total (gives normalized pairwise
comparison matrix)
Step 3: Compute average of elements in
each row (gives estimate of relative priorities
of elements being compared)
Step 2 - Synthesization
RENT
Apt 1
Apt 2
Apt 3
Apt 1
1
4
1/3
Apt 2
¼
1
1/7
Apt 3
3
7
1
SUM
17/4
12
31/21
Next… divide each element by column total
Step 2 - Synthesization
RENT
Relative priorities
Apt 1
Apt 2
Apt 3
Avg
Apt 1
.235
.334
.226
.266
Apt 2
.059
.083
.097
.080
Apt 3
.706
.583
.677
.654
Normalized pairwise comparison matrix
AHP – Relative Priorities
Relative Priorities for Rent
Apt. 1
.266
Apt. 2
.080
Apt. 3
.654
What do
these mean?
AHP – Relative Priorities
Relative Priorities for Rent
Apt. 1
.266
Apt. 2
.080
Apt. 3
.654
These mean that with
respect to Rent, Apt. 3 is
preferred first (65%), then
Apt. 1 (27%), then Apt. 2
(8%)
Step 2 - Synthesization
SIZE
Apt 1
Apt 2
Apt 3
Apt 1
1
1/6
1
Apt 2
6
1
6
Apt 3
1
1/6
1
SUM
8
8/6
8
Next… divide each element by column total
Step 2 - Synthesization
SIZE
Relative priorities
Apt 1
Apt 2
Apt 3
Avg
Apt 1
.125
.125
.125
.125
Apt 2
.75
.75
.75
.75
Apt 3
.125
.125
.125
.125
Normalized pairwise comparison matrix
Step 2 - Synthesization
PROXIMITY
Apt 1
Apt 2
Apt 3
Apt 1
1
5
8
Apt 2
1/5
1
3
Apt 3
1/8
1/3
1
SUM
53/40
19/3
12
Next… divide each element by column total
Step 2 - Synthesization
PROXIMITY
Relative priorities
Apt 1
Apt 2
Apt 3
Avg
Apt 1
.755
.790
.667
.737
Apt 2
.151
.158
.25
.186
Apt 3
.094
.053
.083
.077
Normalized pairwise comparison matrix
AHP - Steps
1. Make pairwise comparisons
2. Synthesize judgments
3. Check for consistency
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AHP – Step 3
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A key step in the making of several pairwise
comparisons is considering the consistency
of the pairwise judgements.
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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