analytic network process (anp) - bpmsg · analytic network process (anp) the analytic network...

Analytic NetworkProcess (ANP)

Klaus D. Goepel Feb. 2011


The analytic network processANP is a decision findingmethod

Overview

Developed by Prof. Thomas L. Saaty

The Analytic Network Process ANP is a decision making method1

Analytic Network Process (ANP)

Goal

Criterion 1 Criterion 3

Alternative 2Alternative 1

Criterion 2

or



The analytic network processANP is a decision findingmethod and generalizationof the analytic hierarchy pro-cess AHP.

OverviewThe Analytic Network Process ANP is a decision making method1


ANP is a generalization of the Analytic Hierarchy Process AHP2




OverviewThe Analytic Network Process ANP is a decision making method1


ANP is a generalization of the Analytic Hierarchy Process AHP2

Goal

CriteriaSub-criteria

Alternatives

Cluster 2

Alternatives

Control Criterion

Cluster 1

AHP ANP




ANP can model complexdecision problems, where ahierarchical model – as usedin AHP – is not sufficient.

OverviewThe Analytic Network Process ANP is a decision making method

ANP is a generalization of the Analytic Hierarchy Process AHP

1


2

ANP can model complex decision problems3


01 New Solutions

02 Value Add

03 NewCustomers

04 ReplaceCompetition

05 AlternativeSales Channels

06 New Appl./Market Segments

Growth StrategiesNetwork Model ANP

simplified 39%

32%

17%

7%

4%

1%



ANP can model complexdecision problems, where ahierarchical model – as usedin AHP – is not sufficient.ANP allows for feedbackconnections and loops.



ANP can model complex decision problems

1


2

3

It allows for feedback connections and loops4

Goal

Cluster B

Cluster A




ANP can model complexdecision problems, where ahierarchical model – as usedin AHP – is not sufficient.ANP allows for feedbackconnections and loops.



ANP can model complex decision problems

1


2

3

It allows for feedback connections and loops4


Overview

Hire

SalesTechnical Experience

Candidate 1 Candidate 2

Example

Decision for the selection of acandidate in recruitment of asales engineer


Overview

Hire



In AHP you do a pair-wisecomparison of criteria andsub-criteria, resulting in localpriorities or weighting factors.

Hierarchical Model (AHP)


Hire



Overview

Candidate 2Candidate 1

Hire

Technical Sales Experience

Goal

CriteriaSub-criteria

Alternatives

59%25%16%

48%52%

In AHP you do a pair-wisecomparison of criteria andsub-criteria, resulting in localpriorities or weighting factors.

By applying the global priori-ties to alternatives, you finallyget a ranking of alternativeswith respect to these criteriaand sub-criteria.

It’s a top-down structure fromthe overall objective tocriteria, from criteria to sub-criteria down to alternatives.

Hierarchical Model (AHP)


In ANP criteria, sub-criteriaand alternatives are treatedequally as nodes in anetwork.

Each of these nodes mightbe compared to any othernode, as long as there is arelation between them.

Overview

Network Model (ANP)

Hire

Technical Experience


Sales


Hire



Control Criteria

Alternatives

In ANP criteria, sub-criteriaand alternatives are treatedequally as nodes in anetwork.

Each of these nodes mightbe compared to any othernode, as long as there is arelation between them.

For example, the ranking ofalternatives might not onlydepend on the weighting ofcriteria, but also givenalternatives can influencethe ranking of criteria.

Overview

Network Model (ANP)

Given Alternatives can influence the weighting of criteria

Criteria


Performance



Soft Skills

Alternatives

Control Criterion

Hard Skills

40%60%

In contrast to AHP, wherehigher level elementsconnect to lower levels –i.e. criteria to sub-criteria –in ANP nodes might begrouped in clusters.

Beside local priorities in thecomparison of one node toa set of other nodes, youmight also introduce clusterpriorities with respect to thegoals.

Overview

Network Model

Clusters and Nodes

59%25%16%


The Super Matrix

Hire



Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria

The network of ANP isrepresented as a matrix.

The matrix is composed bylisting all nodes horizontallyand vertically,

Sales


The Super Matrix

Hire



Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x

Sales Each non-zero element of thematrix represents the con-nection & weight from onenode (columns-header)to another node (row-header)of the network.



The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x

Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x

Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


xHire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x

Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


xHire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


x

Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

Criteria


Super Matrix

The matrix is called Super-Matrix

Hire






The Super Matrix

Crit

eria

Technical

Sales

Experience

Hire

Candid 1

Candid 2Alte

rn.

Tech

nica

l

Sale

s

Expe

rienc

e

Altern.

Can

did

1

Can

did

2

Hire

CriteriaHierarchy Model

Super Matrix

The comparison of nodes –connected to others – followsthe same principal andmethod as in AHP.

Hire



Sales


The Super Matrix

Hire



59%25%16%

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

1625

59

Sales Skills are equally to moderatelymore important than Technical Skills (2x)

Experience is moderatelymore important than Technical Skills (3x)

Experience is moderatelymore important than Sales Skills (3x)

Comparison of Criteria wrt Hire:


The so found priorities arethen arranged as columnvectors in the super-matrix.

Hierarchy Model

Super Matrix

Priority Vector resultingfrom pair-wise comparisons

Priority Vector resultingfrom pair-wise comparisons

Local priorities result fromthe Eigenvector of the com-parison matrix.

2

1/2

3

1/3

3

1/3

Comparison Matrix wrt Hiring

Technical

Sales

Experience


The Super Matrix

Hire



Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

50

50

1625

59

50%50%Candidate 1 has equallytechnical Skills as Candidate 2 (1)

Comparison of Candidates wrtTechnical Skills

Hierarchy Model

Super Matrix

1

1Candidate 1

Candidate 2

Comp. Matrix wrt Technical





The Super Matrix

Hire



Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

50

50

20

80

1625

59

80%20%Candidate 2 has moderately tostrongly better Sales Skills thanCandidate 1 (4x)

Comparison of Candidates wrtSales Skills

Hierarchy Model

Super Matrix

4

1/4Candidate 1

Candidate 2

Comp. Matrix wrt Sales





The Super Matrix

Hire



Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

50

50

20

80

1625

59

67

33

33%67%Candidate 1 has equally toModerately better Experience thanCandidate 2 (2x)

Comparison of Candidates wrtExperience

Hierarchy Model

Super Matrix

1/2

2Candidate 1

Candidate 2

Comp. Matrix wrt Experience





The Super Matrix

Hire



Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

50

50

20

80

1625

59

67

33

Candid 1

Candid 2

52

48Alte

rn.

Hierarchy Model

Unweighted Super Matrix

52% 48%

Result: Priorities ofAlternatives






The Super Matrix

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

Hire



50

50

20

80

1625

59

67

33

Network Model

Super Matrix

Impact of Alternativeson the priorities

of criteria





The Super Matrix

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

Hire


Candidate 2

75

13

13

Candidate 1

50

50

20

80

1625

59

67

33

13%75% 13%Technical Skills are strongly to verystrongly more prevalent than Sales Skills (6x)

Technical Skills are strongly to verystrongly more prevalent than Experience (6x)

Sales Skills are equally to Experience (1)

Comparison of Criteria wrtCandidate 1

Network Model

Super Matrix


of criteria

1/6

6

1/6

6

1

1

Technical

Sales

Experience

Comp. Matrix wrt Candidate 1





The Super Matrix

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

Hire


Candidate 2

13

75

13

Candidate 1

50

50

20

80

1625

59

67

33

75%13% 13%Sales Skills are strongly to verystrongly more prevalent than Technical Skills (6)

Sales Skills are strongly to verystrongly more prevalent than Experience (6)

Technical Skills are equally to Experience (1)

Comparison of Criteria wrtCandidate 2

Super Matrix

Network Model

75

13

13


of criteria

6

1/6

1

1

1/6

6

Technical

Sales

Experience

Comp. Matrix wrt Candidate 2





The Super Matrix

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

Hire


Candidate 2

75

13

13

13

75

13

Candidate 1

50

50

20

80

1625

59

67

33

After all comparisons aredone, we get the“Unweighted Super Matrix”

Network Model

This matrix is then normalizedi.e. the sum of all columns isscaled to 1100 100 100 100 100 100

Weighted Super Matrix


The Super Matrix

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

Hire


Candidate 2

75

13

13

13

75

13

Candidate 1

50

50

20

80

1625

59

67

33

Candid 1

Candid 2

36

64Alte

rn.

1826

6

1826

6

1826

6

18

32

18

32 36% 64%

After all comparisons aredone, we get the“Unweighted Super Matrix”

The whole model is synthe-sized by calculating the“Limit Matrix”. The LimitMatrix is the weightedSuper matrix, taken to thepower of k+1, where k is anarbitrary number.


Network Model

Limit Matrix

(k+1)

This matrix is then normalizedi.e. the sum of all columns isscaled to 1




Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



Why changes the ranking ofCandidate 2 from two in thehierarchy model to one in theNetwork model?

Why changes the ranking of Candidate 2from two in the Hierarchy modelto one in the Network model ?


Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



33%67%

Both candidates have therequired experience



Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



33%67%

- candidate 1 slightly morethan candidate 2.




Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



67%

59%


Experience is given a relativehigh weight




Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



67%

59%

Resulting in the slightly higherranking for candidate 1 in thehierarchical model.


Experience is given a relativehigh weight




Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



75%13% 13%

In the network model we alsolook at each candidate’s skillsindependent from the othercandidate



Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



75%13% 13%

In the network model we alsolook at each candidate’s skillsindependent from the othercandidateNow we see the outstandingsales skills of candidates 2



Overview

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


Hire



75%

25%

In the network model we alsolook at each candidate’s skillsindependent from the othercandidateNow we see the outstandingsales skills of candidates 2Finally in the network model,sales skills get more weightin the decision than theexcellent technical skillsof candidate 1



Overview

Hire



75%

25%

Tech

nica

l

Sale

s

Expe

rienc

e

Crit

eria

Technical

Sales

Experience

Hire

Altern.

Can

did

1

Can

did

2Candid 1

Candid 2Alte

rn.

Hire

Criteria

75

13

13

13

75

1350

50

20

80

1625

59

67

33


In the network model we alsolook at each candidate’s skillsindependent from the othercandidateNow we see the outstandingsales skills of candidates 2Finally in the network model,sales skills get more weightin the decision than theexcellent technical skillsof candidate 1



Control HierarchiesA decision network can bearranged under a control hier-archy of benefits and costs

Hire



Salary


Benefits Costs

OverallObjectiveTwo Layer Benefit/Cost Model

In our example here, we al-ready evaluated the benefitsof hiring – with respect to thehard – and soft-skills of thetwo candidates.

80% 20%

We can now evaluate therequested salary of bothcandidates under controlcriterion costs.Depending on our overallobjective, either benefits orcosts could be assigned ahigher weighting.

Layer 1

Layer 2


Control Hierarchies

Hire



Salary


Benefits Costs

OverallObjectiveTwo Layer Benefit/Cost Model

80% 20%

We have now a two layermodel with a control hierarchy– benefits and costs – and asub-network under benefitsand a hierarchy under costs.Ranking of alternatives in atwo layer model can beevaluated using a ratioformula Benefit/Cost or anadditive formula (B-C)

Benefits/Costs (B/C)

Benefits - Costs (B-C)

Evaluation Formulas



Sub-networkOpportunities

Control Hierarchies

Hire



Salary


Benefits Costs

OverallObjective

Opportunities Risks


Sub-networkRisks

Two Layer BOCR Model

(B*O) / (C*R)

(B+O)- (C-R)

Evaluation Formulas

The control hierarchy couldbe extended with additionalcontrol parameter, e.g. op-portunities and risks, to builda two layer BOCR model.


Klaus D. Goepel Feb. 2011

analytic network process (anp) - bpmsg · analytic network process (anp) the analytic network...

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