The Analytic Network Process for decision making with dependence and feedback

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The Analytic Network Process for decision making
with dependence and feedback
The SUPER DECISIONS Software
By Creative Decisions Foundation
4922 Ellsworth Avenue Pittsburgh,
PA 15213 Phone [phone]
Fax [phone]
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SuperDecisions software public site www.superdeci
sions.com SuperDecisions software and other
materials on Toms site for students www.superdec
isions.com/saaty
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To Build a Simple Network Model

• Create the clusters and the nodes inside the
  clusters.
• Link the nodes. Select a node (parent) and link
  it to other nodes (children) that it influences
  or that influence it. A parent may have children
  in many different clusters. The parent and its
  children from each cluster form a pair-wise
  comparison set.
• Clusters are linked automatically when nodes in
  them are linked.

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Create the Clusters and the Nodes
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Link the nodes in the Criteria cluster to nodes
in the Alternatives cluster
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Link the Nodes the Other Way (Alternative nodes
to Criteria nodes)
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Make Comparisons

• Compare the cars for preference with respect to
  price, MPG, Prestige and Comfort (same as in a
  hierarchy)
• Compare the criteria for preference with respect
  to each alternative car What is better about the
  Carryon, its price (UGH!) or its prestige
  (YEAH!)?

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Establishing Priorities for Criteria

• In AHP criteria are prioritized by answering the
  question, How important is C1 compared to C2
  with respect to the goal? Sometimes too abstract
  a question to answer.
• In ANP criteria are prioritized by asking how
  important they are in each of the alternatives
  being considered. Usually an easier question to
  answer when looking at actual alternatives that
  have the properties in question.

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Pairwise Compare Cars wrt Criteria
Example Pairwise Comparisons for cars with
respect to Prestige and Comfort
Results for Prestige
Results for Comfort
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Pairwise Compare Criteria wrt Cars
Example Pairwise Comparisons criteria with
respect to Avalon
Results for Avalon
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The results of all the pairwise comparisons make
up the unweighted supermatrix. For example, the
last 4 numbers in column 1 below come from
comparing the criteria with respect to Avalon.
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The limit supermatrix is obtained by raising the
weighted supermatrix to powers until it converges
(in this case all columns are same).
Limit Supermatrix
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Final results for car model
From ANP using Super Decisions
From AHP using Expert Choice
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Why are the results different?

• In AHP the user, going top-down making
  comparisons, and when asked without reference to
  the alternatives, over-estimated the importance
  of cost to him.
• In ANP the user learned through feedback
  comparisons that his priority for cost was not
  nearly as high as he believed when asked the
  question abstractly a 24,000 car today is in
  the same price category as an 18,000 car and the
  other comparisons brought that information out.

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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.

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We can add inner dependence price is influenced
by prestige and comfort prestige is influenced
by price and comfort.
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An Example of an Inner Dependent Comparison is
shown below Which influences Prestige more,
Price or Comfort?
The results are (with inner dependence)
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• Other Concepts Important in the ANP
• Multipart models
• Strategic Criteria
• BOCR merits and their Control Criteria
• One decision network with feedback for each
  control criterion - all comparisons made with
  regard to the control criterion

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SuperDecisions software public site www.superdeci
sions.com SuperDecisions software and other
materials on Toms site for students www.superdec
isions.com/saaty