Designing Analytic Network Process

Published Date: 02 Nov 2017

In regard to this research’s goal, at first we attempt to design proper network process model base on SMI criteria and sub-criteria in Super Decision software. Following figure shows ANP diagram base on this model.

ANP diagram – criteria and sub-criteria priority in super decision software

Criteria

Symbol

Sub Criteria

Symbol

Agility

C1

Awareness/Visibility

S11

Flexibility

S12

Adaptability

S13

Capacity/Elasticity

S14

Costs

C2

Acquisition

S21

On-Going

S22

Risk

C3

Provider

S31

Compliance

S32

HR

S33

Security

C4

Physical & Environmental

S41

Communication & Operation

S42

Access Control

S43

Data

S44

Quality

C5

Serviceability

S51

Availability

S52

Functionality

S53

Effectiveness

S54

Capability

C6

Function #1

S61

Function #n

S62

Criteria and sub-criteria and associated symbols

Because in this research we use the assessment of more than one expert, geometric mean technique is used to prioritize their point of view. Geometric mean is the most appropriate mathematics rule for combining assessments in AHP, because it maintains inverse property of pairwise comparison matrices. .(اکزل و ساعتي، 1983 : 102) In addition to considering each member of expert group’s assessment, it will help to measure the assessment of the entire group for each pairwise comparison.

Main Criteria’s Pairwise Comparison base on the goal (W21)

In this research, six main criteria as main decision criteria are selected. Therefore, at the first step criteria’s pairwise comparison has been covered. The following table shows the result of performing pairwise comparison.

 

C1

C2

C3

C4

C5

C6

G

EV

C1

1

0.240

0.247

0.149

0.209

1.431

0.372

0.051

C2

4.169

1

2.187

0.574

1.046

3.728

1.653

0.226

C3

4.043

0.457

1

0.871

2.702

3.438

1.570

0.214

C4

6.722

1.741

1.149

1

2.952

4.762

2.396

0.327

C5

4.789

0.370

0.370

0.339

1

3.245

0.947

0.129

C6

0.699

0.268

0.291

0.210

0.308

1

0.390

0.053

Main criteria’s pairwise comparison’s matrix

Therefore, Eigenvector W21 will be as follow:

0.051

0.226

0.214

0.327

0.129

0.053

W21=

The calculated inconsistency rate is: 0/074 which demonstrates performed pairwise comparisons are desirable. Output of Super Decision software for prioritizing main criteria base on research goal is demonstrated in following picture.

Prioritizing main criteria base on research goal with Super Decision software

As observed, base on research goal, criterion C4 with the normal weight of 0.327 has the most priority. Also Criteria C2 and C3 with the similar importance have second and third priority. Criterion C5 has forth priority and criteria C1 and C6 with similar weight of 0.051 and 0.053 have the least priority.

Main Criteria interdependencies’ Pairwise Comparison (W22)

In the next step, to get W22 super matrix, interdependencies for main criteria must be calculated. For this reason DEMATEL technique is used. Accordingly, experts are able to express their viewpoint of effects (direction and intensity) between criteria with more control. In is necessary to mention that this technique not only show us initial effects but also it is able to demonstrate the causal effect between each pair of criteria in the system by drawing influence map.

Calculating the Initial Direct-Relation Matrix (M)(average matrix)

Each expert is asked to signify the grade to which he or she believes a criterion i affects criterion j. The pairwise comparisons between any two factors are specify as aij and are given an integer grade ranging from 0, 1, 2, 3, and 4, representing ‘No influence (0),’ ‘Low influence (1),’ ‘Medium influence (2),’ ‘High influence (3),’ and ‘Very high influence (4),’ respectively. In the case of having group of experts, arithmetic mean will be used to calculate initial direct-relation matrix.

 

Agility

Costs

Risk

Security

Quality

Capability

Agility

0

2

1

2

2

2

Costs

3

0

3

3

4

4

Risk

1

1

2

1

2

2

Security

2

4

3

3

3

1

Quality

1

3

1

2

2

1

Capability

1

3

1

1

1

0

Initial direct-relation matrix (M) for main criteria

Calculate the normalized initial direct-relation matrix ()

The normalized initial direct-relation matrix N is obtained by normalizing the average matrix M in the following way:

Let

Then

Since the sum of each row j of matrix M represents the total direct effects that criterion i gives to the other criteria, represents the total direct effects of the criterion with the most direct effects on others. Likewise, since the sum of each column i of matrix M represents the total direct effects received by criterion i, represents the total direct effects received of the factor that receives the most direct effects from others. The positive scalar k takes the lesser of the two as the upper bound, and the matrix N is obtained by dividing each element of M by the scalar k. Note that each element of matrix N is between zero and less than 1.

Base on Matrix M, scalar k is equal to 17 and normalized matrix is demonstrated as follows:

 

Agility

Costs

Risk

Security

Quality

Capability

Agility

0.000

0.118

0.059

0.118

0.118

0.118

Costs

0.176

0.000

0.176

0.176

0.235

0.235

Risk

0.059

0.059

0.118

0.059

0.118

0.118

Security

0.118

0.235

0.176

0.176

0.176

0.059

Quality

0.059

0.176

0.059

0.118

0.118

0.059

Capability

0.059

0.176

0.059

0.059

0.059

0.000

Normalized matrix N for main criteria

Computing the total relation matrix

A continuous reduction of the indirect effects of problems along the powers of matrix N, e.g., , , …, , guarantees convergent solutions to the matrix inverse. The total relation matrix T is an n x n matrix and is defined as follow:

Note that and , where 0 is the n x n null matrix and I is the n x n identity matrix.

 

Agility

Costs

Risk

Security

Quality

Capability

Agility

0.152

0.343

0.255

0.329

0.364

0.287

Costs

0.402

0.396

0.485

0.517

0.627

0.500

Risk

0.185

0.260

0.286

0.240

0.331

0.268

Security

0.382

0.619

0.527

0.555

0.623

0.381

Quality

0.233

0.425

0.285

0.364

0.406

0.265

Capability

0.186

0.343

0.224

0.238

0.271

0.159

Total relation matrix T for main criteria

Obtaining the network-relations-map

In order to clarify the structural relation between criteria while balancing the complexity of the system to a convenient degree, it is essential to set a threshold value p to extract some insignificant effects in matrix T. as long as each criterion of matrix T gives information on how one criterion affects another, it is essential for the management group (decision-makers) to set a threshold value to decrease the complexity of the structural relation model implied in matrix T. therefore, only some criteria, which’s effect in matrix T is greater than the threshold value, must be chosen and presented in an network-relations-map (NRM) (Tzeng et al., 2007).

In this research, the threshold value has been calculated equal to 0.35. while the threshold value has been calculated, the final result can be demonstrated in an NRM as below:

 

Agility

Costs

Risk

Security

Quality

Capability

Agility

0

0

0

0

0.364

0

Costs

0.402

0

0.485

0.517

0.627

0.500

Risk

0

0

0

0

0

0

Security

0.382

0.619

0.527

0

0.623

0.381

Quality

0

0.425

0

0.364

0

0

Capability

0

0

0

0

0

0

NRM for main criteria

The cluster interdependencies map is demonstrated below:

Capability

Quality

Risk

Costs

Agility

Security

Producing a causal diagram

D

R

D+R

D-R

Agility

1.729

1.540

3.269

0.189

Costs

2.927

2.386

5.312

0.541

Risk

1.569

2.061

3.630

-0.491

Security

3.088

2.243

5.331

0.845

Quality

1.978

2.622

4.600

-0.644

Capability

1.420

1.859

3.280

-0.439

Causal diagram for main criteria

The sum of indices in each row (D) denotes degree of effect, given by that criterion on other criteria in the system. In this case Security has the most effect given. After that Costs with approximately equivalent effect given is in second place. Quality and Agility criteria are also having equivalent effect given and placed in lower level and after them Risk and Capability.

The sum of each column (R) denotes degree of effect, received by that criterion on other criteria in the system. Base on this Quality hast the most effect received by other criteria. Agility criterion has the least effect received from other criterion.

The horizontal axis vector (D + R) called Prominence, which specifies the degree of relative importance of each criterion. In other words, if the value of D + R for particular criterion be higher, that criterion has more interaction with other criteria in the system. Base on this Cost and Security criteria having the most interaction with other criteria that are covered. Also Agility and Capability criteria having the least interaction with other criteria in the system.

The vertical axis vector (D – R) called relation and may assign criteria in cause and effect groups. Generally, When (D – R) is positive, that particular is a net causer, and when (D – R) is negative, is a net receiver. In this model Agility, Cost and Security are the causer criteria and Risk, Quality and Capability are receiver.