Analytic Network Process: Decision Making and Feedback
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The Analytic
Network Process
Decision Making with Dependence and Feedback
G
O
A
L
Price
MPG (miles
per gallon)
Prestige
Comfort
Toyoto Camry
Acura TL
Honda Civic
C
R
I
T
E
R
I
A
A
L
T
E
R
N
A
T
I
V
E
S
Hierarchic
Thinking
Changing from a Hierarchical
Model to a Network Model
Price
MPG (miles
per gallon)
Prestige
Comfort
Toyoto Camry
Acura TL
Honda Civic
C
R
I
T
E
R
I
A
A
L
T
E
R
N
A
T
I
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Network Model with Feedback
Network Models do not have Goals
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Establishing Priorities for Criteria
In AHP one answers the question: “How
important is Criterion1 compared to Criterion2
with respect to the goal?”
Sometimes too abstract a
question to answer.
In ANP criteria are prioritized by asking how
important they are in the alternatives being
considered.
Usually an easier question to answer when looking
at actual alternatives that have the properties in question.
.707
.070
.223
Cars compared with respect to
Prestige (
and similarly for the other
criteria)
Feedback: Link Alternatives to Criteria and
compare for Preference
For example, a pairwise question would be: “For the Acura TL,
which do you like better, its prestige or its price?” ; “Its prestige or
its MPG?” etc.
.499
.066
.079
.355
Make Comparisons
For each car pairwise compare
the criteria for importance to
establish the priorities of the
criteria in that car: Prestige,
Price, MPG, and Comfort
This results in a vector of
priorities of the criteria for each
car.
Pairwise Compare Criteria for each Car
Results for Acura TL
Results for Toyota Camry
Acura TL
Toyota Camry
Pairwise Compare Criteria wrt Cars
Results for Honda Civic
Honda Civic
The Unweighted Supermatrix
For example, the priorities in the last column come from
comparing the criteria with respect to the Honda Civic. That
is, what we value most about the Honda is its price.
The limit supermatrix is obtained by raising the weighted supermatrix to powers
until it converges (in this case all columns are the same, though not always true).
Limit Supermatrix
ANP
AHP
Acura TL
.457
.344
Toyota Camry
.173
.200
Honda Civic
.369
.455
The final answer, the
synthesis, below is
obtained by normalizing
the raw values for the
alternatives from the limit
supermatrix:
Why are the results different?
•
In AHP
– the user, going top-down making
comparisons, when asked without referring
to actual alternatives, over-estimated the
importance of cost.
•
In ANP
– the user learned through feedback
comparisons that his/her priority for Cost is
not nearly as high as originally thought when
asked the question abstractly, while Prestige
gets more weight.
This is why a husband and wife, setting out to the dealership to buy a “sensible” low
priced car, walked out with something entirely different and much more costly.
When they saw the shiny cars on the showroom floor they revised their priorities.
Inner and Outer Dependence
•
Outer dependence
- the parent node and
the nodes to be compared are in different
clusters. A directed link appears
from
the
parent node cluster to the other cluster.
•
Inner dependence
- the parent node and
the nodes to be compared are in the same
cluster. The cluster is linked to itself and a
loop link appears.
We can add some inner dependence: eg, price
is influenced by prestige and comfort; and
prestige is influenced by price and comfort.
An Example of an Inner Dependent
Comparison is shown below:
Which influences Price more, Prestige or Comfort?
Which influences Prestige more, Price or Comfort?
The results with the interdependencies in
place are:
ANP
ANP
AHP
(With inner
(No inner
dependencies)
dependence)
Acura TL
.487
.457
.344
Toyota Camry
.182
.173
.200
Honda Civic
.331
.369
.455
Explore the Analytic Network Process for decision-making with dependence and feedback. Compare hierarchical and network models, prioritize criteria in AHP and ANP, establish car priorities based on criteria, and employ feedback to link alternatives to criteria for preference. Make pairwise comparisons to determine criteria importance and car priorities effectively.
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Presentation Transcript
The Analytic Network Process Decision Making with Dependence and Feedback
Hierarchic GOAL Thinking CRITERIA MPG (miles per gallon) Prestige Price Comfort ALTERNATIVES Acura TL Toyoto Camry Honda Civic
Changing from a Hierarchical Model to a Network Model
Network Model with Feedback CRITERIA MPG (miles per gallon) Price Prestige Comfort ALTERNATIVES Acura TL Toyoto Camry Honda Civic
Network Models do not have Goals A network model has a criteria cluster and an alternatives cluster, but no goal. Step 1. Compare the alternatives with respect to each criterion (like we do in AHP models). Step 2. Compare the criteria with respect to each of the cars to get a profile of how important the criteria are for each car. Step 3. Synthesize to get the overall priorities for the cars, and, incidentally, for the criteria (for these cars)
Establishing Priorities for Criteria In AHP one answers the question: How important is Criterion1 compared to Criterion2 with respect to the goal? Sometimes too abstract a question to answer. In ANP criteria are prioritized by asking how important they are in the alternatives being considered. Usually an easier question to answer when looking at actual alternatives that have the properties in question.
Cars compared with respect to Prestige (and similarly for the other criteria) .707 .070 .223
Feedback: Link Alternatives to Criteria and compare for Preference For example, a pairwise question would be: For the Acura TL, which do you like better, its prestige or its price? ; Its prestige or its MPG? etc. .499 .066 .079 .355
Make Comparisons For each car pairwise compare the criteria for importance to establish the priorities of the criteria in that car: Prestige, Price, MPG, and Comfort This results in a vector of priorities of the criteria for each car.
Pairwise Compare Criteria for each Car Results for Acura TL Acura TL Results for Toyota Camry Toyota Camry
Pairwise Compare Criteria wrt Cars Honda Civic Results for Honda Civic
The Unweighted Supermatrix For example, the priorities in the last column come from comparing the criteria with respect to the Honda Civic. That is, what we value most about the Honda is its price.
Limit Supermatrix The limit supermatrix is obtained by raising the weighted supermatrix to powers until it converges (in this case all columns are the same, though not always true). The final answer, the synthesis, below is obtained by normalizing the raw values for the alternatives from the limit supermatrix: ANP AHP Acura TL .457 .344 Toyota Camry .173 .200 Honda Civic .369 .455
Why are the results different? In AHP the user, going top-down making comparisons, when asked without referring to actual alternatives, over-estimated the importance of cost. In ANP the user learned through feedback comparisons that his/her priority for Cost is not nearly as high as originally thought when asked the question abstractly, while Prestige gets more weight. This is why a husband and wife, setting out to the dealership to buy a sensible low priced car, walked out with something entirely different and much more costly. When they saw the shiny cars on the showroom floor they revised their priorities.
Inner and Outer Dependence Outer dependence - the parent node and the nodes to be compared are in different clusters. A directed link appears from the parent node cluster to the other cluster. Inner dependence - the parent node and the nodes to be compared are in the same cluster. The cluster is linked to itself and a loop link appears.
We can add some inner dependence: eg, price is influenced by prestige and comfort; and prestige is influenced by price and comfort.
An Example of an Inner Dependent Comparison is shown below: Which influences Price more, Prestige or Comfort? Which influences Prestige more, Price or Comfort?
The results with the interdependencies in place are: ANP ANP AHP (With inner (No inner dependencies) dependence) Acura TL .487 .457 .344 Toyota Camry .182 .173 .200 Honda Civic .331 .369 .455
