ANALYTIC NETWORK PROCESS - My LIUCmy.liuc.it/MatSup/2010/N90212/_Lezione_MMAI_CC.pdf · Analytic...
Transcript of ANALYTIC NETWORK PROCESS - My LIUCmy.liuc.it/MatSup/2010/N90212/_Lezione_MMAI_CC.pdf · Analytic...
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“Metodi Matematici per le applicazioni industriali”
Facoltà di Ingegneria
ANALYTIC NETWORK PROCESS
Facoltà di Ingegneria
ANALYTIC NETWORK PROCESSDecision making with dependence and feedback
Ing. Claudia ColicchiaIng. Claudia [email protected]
ANPANP
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Introduction
Profesor Thomas L. Saaty 90´sGeneralization of AHPGeneralization of AHP.ANP allows to include relations of dependence and feedback among elements of the system.The problem modelization is more complex and more realistic.
Thomas L. Saaty “Decision making with independence and feedback: The Analytic Network Process” RWS Publications, Pittsburgh (2001)
ANPANP
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Analytic Hierarchy Process: One- direction influence
ANPANP
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Analytic Network Process (ANP): Interdependence and feedback
ANPANP
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Analytic Network Process (ANP): Network model
ANPANP
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Network model
ANPANP
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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
th l tother 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.
ANPANP
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Example: Changing from a Hierarchy to a Network Model
ANPANP
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Network Models do not have goals
A network model has a criteria cluster and an
alternatives cluster, but no goal.
ANPANP
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Evaluation methodology based on ANP
1. MODELIZATION OF THE PROBLEM AS A NETWORK
2 WEIGHTING OF THE ELEMENTS BY MEANS OF ANP2. WEIGHTING OF THE ELEMENTS BY MEANS OF ANP
ANPANP
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MODELIZATION OF THE PROBLEM AS A NETWORK
i. Identification of the elements of the network (criteria and alternatives)
ii Grouping of the elements into clustersii. Grouping of the elements into clusters
iii. Analysis of the influences within the networky
ANPANP
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Influence matrix
ANPANP
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Influence matrix
ANPANP
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Influence matrix
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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Influence matrix - example
ANPANP
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WEIGHTING OF THE ELEMENTS BYMEANS OF ANP
i. Calculate priorities among elements
ii. Calculate priorities among groups
iii. Build original supermatrix
iv Calculate weighted supermatrixiv. Calculate weighted supermatrix
v. Calculate limit supermatrix
vi. Obtain alternatives prioritization
ANPANP
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i. Calculate priorities among elements
ANPANP
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i. Calculate priorities among elements
QUESTION: Given two elements of component C2 which have an influence on the element e11, How much more does the first element influence on the ,element e11than the second element?
ANPANP
PRIORITIES ARE OBTAINED THE SAME WAY AS FOR AHP.
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i. Calculate priorities among elements
ANPANP
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i. Calculate priorities among elements
ANPANP
SAME PROCEDURE FOR ALL THE ELEMENTS OF THE NETWORK.
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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 answeralternatives being considered. Usually an easier question to answer when looking at actual alternatives that have the properties in question.
ANPANP
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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.
For each car pairwise pcompare the criteria for importance to establish the priorities of the criteria in that
.499
priorities of the criteria in that car: Prestige, Price, MPG, and Comfort
.066
.079355
This results in a vector of priorities of the criteria for each car..355
ANPANP
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Cars compared with respect to Prestige
(and similarly for the other criteria)
.707
.070
.223
ANPANP
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ii. Calculate priorities among groups
ANPANP
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ii. Calculate priorities among groups
QUESTION: Given two groups of the system, C2 and C4, which have an influence on group C1, How much more does C2 influence on C1 than C4?g p ,
ANPANP
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ii. Calculate priorities among groups
ANPANP
SAME PROCEDURE FOR ALL THE CLUSTERS OF THE NETWORK.
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iii. Build original supermatrix
ANPANP
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iii. Build original supermatrix
ANPANP
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Example: 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.
ANPANP
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iv. Calculate weighted supermatrix
ANPANP
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iv. Calculate weighted supermatrix
ANPANP
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v. Calculate limit supermatrix
ANPANP
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v. Calculate limit supermatrix
ANPANP
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Limit SupermatrixThe 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 normalizingobtained by normalizing the raw values for the alternatives from the limit
t isupermatrix:
ANP AHP
Acura TL 457 344Acura TL .457 .344
Toyota Camry .173 .200
H d Ci i 369 455
ANPANP
Honda Civic .369 .455
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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.abs ac y, e es ge ge s o e e g
This is why a husband and wife, setting out to the dealership to buy a “sensible” l i d lk d t ith thi ti l diff t d h tllow 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.
ANPANP
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ANP vs. AHP:
AdvantagesMore creative and flexible it does not need a strict hierarchy to order theMore creative and flexible, it does not need a strict hierarchy to order the elements.It allows a closer model to reality.Results more precise and objective.
DisadvantagesThe higher complexity of the problem requires more calculationsMore time and effort are required
ANPANP
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We can add some inner dependence: eg, price is influenced by prestige and comfort; and prestige is influenced by price and comfort.
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Inner Dependent Comparison
Which influences Price more, Prestige or Comfort?
Which influences Prestige more, Price or Comfort?
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