The 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 can map out 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 indicate the degree to which he or she believes a criterion i affects criterion j. These pairwise comparisons between any two factors are denoted by aij and are given an integer score 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 decrease of the indirect effects of problems along the powers of matrix N, e.g., , , …, , guarantees convergent solutions to the matrix inversion similar to an absorbing Markov chain matrix. Note that and , where 0 is the n x n null matrix and I is the n x n identity matrix. The total relation matrix T is an n x n matrix and is defined as follow:

 

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 impact-relations-map

In order to explain the structural relation among the criteria while maintaining the complexity of the system to a manageable level, it is essential to set a threshold value p to filter out some negligible effects in matrix T. While each criterion of matrix T provides information on how one criterion affects another, the decision-maker must set a threshold value in order to reduce the complexity of the structural relation model implicit in matrix T. Only some criteria, which’s effect in matrix T is greater than the threshold value, should be chosen and shown in an impact-relations-map (IRM) (Tzeng et al., 2007).

In this research, the threshold value has been calculated equal to 0.35. As long as the threshold value has been calculated, the final result can be shown in an IRM demonstrated 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

IRM 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 (Tzeng et al. 2007; Tamura et al., 2002). In this model Agility, Cost and Security are the causer criteria and Risk, Quality and Capability are receiver.

Output of DEMATEL Scatter graph for main criteria

Sub-criteria’s pairwise comparison

In the third step SMI’s sub-criteria’s pairwise comparison has been covered. in each step pairwise comparison are applied to sub-criteria related to each main criterion of matrix .

Agility’s sub-criteria pairwise comparison

The result of Agility’s sub-criteria pairwise comparison is demonstrated in following table. Base on acquired result, index S14 with weight 0.369 has the highest priority. Index S13 is in second place and index S12 is in third place. After all index S11 has the lowest priority. Since, inconsistency ratio of applied comparisons is 0.074, acquired results are reliable.

 

S11

S12

S13

S14

G

EV

S11

1

0.488

0.370

0.608

0.576

0.134

S12

2.048

1

0.608

0.425

0.853

0.198

S13

2.702

1.644

1

0.608

1.282

0.298

S14

1.644

2.352

1.644

1

1.588

0.369

Agility’s sub-criteria pairwise comparison

Agility’s sub-criteria priority

Cost’s sub-criteria pairwise comparison

The result of Cost’s sub-criteria pairwise comparison is demonstrated in following table. Base on acquired result, index S21 with normal weight of 0.723 has higher priority than Index S22. Additionally, in comparison of two criteria is always equal to 0, therefore acquired results are reliable.

 

S21

S22

G

EV

S21

1.000

2.605

1.614

0.723

S22

0.384

1.000

0.620

0.277

Cost’s sub-criteria pairwise comparison

Cost’s sub-criteria priority

Risk’s sub-criteria pairwise comparison

The result of Risk’s sub-criteria pairwise comparison is demonstrated in following table. Base on acquired result, index S31 has the highest priority. Index S32 is in second place and index S33 has the lowest priority. Since, inconsistency ratio of applied comparisons is 0.002, acquired results are reliable.

 

S31

S32

S33

G

EV

S31

1

3.245

3.728

2.296

0.624

S32

0.308

1

2.352

0.898

0.244

S33

0.268

0.425

1

0.485

0.132

Risk’s sub-criteria pairwise comparison

Risk’s sub-criteria priority

Security’s sub-criteria pairwise comparison

The result of Security’s sub-criteria pairwise comparison is demonstrated in following table. Base on acquired result, index S44 is the most important index among Security’s sub-criteria and has the highest priority. Indexes S43 and S41 are having the next high priority and index S42 has the lowest priority. Since, inconsistency ratio of applied comparisons is 0.087, acquired results are reliable.

 

S41

S42

S43

S44

ميانگين هندسي

بردارويژه

S41

1

1.059

0.549

0.725

0.806

0.178

S42

0.944

1

0.725

0.249

0.642

0.142

S43

1.821

1.380

1

0.232

0.873

0.193

S44

1.380

4.020

4.317

1

2.212

0.488

Security’s sub-criteria pairwise comparison

Security’s sub-criteria priority

Quality’s sub-criteria pairwise comparison

The result of Quality’s sub-criteria pairwise comparison is demonstrated in following table. Base on acquired result, index S52 is the most important index among Security’s sub-criteria and has the highest priority. Indexes S53 and S51 are having the next high priority and index S54 has the lowest priority. Since, inconsistency ratio of applied comparisons is 0.015, acquired results are reliable.

 

S51

S52

S53

S54

G

EV

S51

1

0.320

0.803

2.048

0.851

0.200

S52

3.129

1

2.048

1.320

1.705

0.401

S53

1.246

0.488

1

1.783

1.020

0.240

S54

0.488

0.758

0.561

1

0.675

0.159

Quality’s sub-criteria pairwise comparison

Quality’s sub-criteria priority

Capability’s sub-criteria pairwise comparison

According to experts’ opinion, both index of Capability criterion have the equal importance. This result is clearly observed in following table and figure. Additionally, in comparison of two criteria is always equal to 0, therefore acquired results are reliable.

 

S61

S62

G

EV

S61

1.000

1.000

1.000

0.500

S62

1.000

1.000

1.000

0.500

Capability’s sub-criteria pairwise comparison

Capability’s sub-criteria priority

Sub-criteria interdependencies’ pairwise comparison:

For reflecting the interdependencies between sub-criteria, DEMATEL technique is used. As we did before, four step should be performed:

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

Because viewpoint of group of expert are used, arithmetic mean will be used to calculate initial direct-relation matrix.

 

Awareness/Visibility

Flexibility

Adaptability

Capacity/Elasticity

Acquisition

On-Going

Provider

Compliance

HR

Physical&Environmental

Communication&Operation

AccessControl

Data

Serviceability

Availability

Functionality

Effectiveness

Function#1

Function#n

Awareness/Visibility

0

1

1

2

2

2

1

1

1

2

1

1

2

1

1

1

1

0

0

Flexibility

1

1

2

1

2

2

2

1

1

2

1

1

1

1

1

1

1

1

1

Adaptability

1

1

0

1

2

2

2

1

1

0

1

0

1

1

1

1

1

1

1

Capacity/Elasticity

1

1

1

1

2

2

1

1

1

2

1

0

1

1

1

1

2

1

1

Acquisition

1

1

2

1

0

1

0

1

1

0

0

0

0

1

1

2

2

1

1

On-Going

1

1

1

2

1

0

1

1

1

1

1

1

1

2

2

2

2

2

2

Provider

1

2

2

2

2

1

2

2

2

2

2

2

3

2

2

2

1

1

1

Compliance

1

1

1

1

2

2

2

0

1

1

1

2

3

1

1

2

2

1

1

HR

1

1

1

1

2

2

1

1

0

1

1

2

3

1

1

1

1

1

1

Physical&Environmental

1

1

1

2

2

2

2

2

2

2

2

2

3

2

3

1

1

1

1

Communication&Operation

1

1

1

1

2

2

1

1

1

2

1

2

3

2

2

1

1

1

1

AccessControl

1

1

1

0

2

2

1

2

2

2

2

1

4

2

2

2

1

1

1

Data

1

1

1

1

2

2

1

3

2

3

2

4

0

2

2

2

1

1

1

Serviceability

1

1

1

2

2

2

2

2

1

2

2

2

2

1

3

2

2

1

1

Availability

1

1

2

1

2

2

2

2

1

2

2

2

2

2

1

2

2

2

2

Functionality

2

1

1

1

2

2

2

2

2

2

2

1

3

1

1

1

2

2

2

Effectiveness

1

1

1

1

2

2

1

1

1

1

1

1

1

1

2

2

1

1

1

Function#1

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

1

Function#n

0

0

0

1

1

1

1

1

1

1

1

1

1

1

1

1

1

1

0

Initial direct-relation matrix (M) for sub-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:

Then

 

S11

S12

S13

S14

S21

S22

S31

S32

S33

S41

S42

S43

S44

S51

S52

S53

S54

S61

S62

S11

0.000

0.029

0.029

0.057

0.057

0.057

0.029

0.029

0.029

0.057

0.029

0.029

0.057

0.029

0.029

0.029

0.029

0.000

0.000

S12

0.029

0.029

0.057

0.029

0.057

0.057

0.057

0.029

0.029

0.057

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

S13

0.029

0.029

0.000

0.029

0.057

0.057

0.057

0.029

0.029

0.000

0.029

0.000

0.029

0.029

0.029

0.029

0.029

0.029

0.029

S14

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.029

0.029

0.057

0.029

0.000

0.029

0.029

0.029

0.029

0.057

0.029

0.029

S21

0.029

0.029

0.057

0.029

0.000

0.029

0.000

0.029

0.029

0.000

0.000

0.000

0.000

0.029

0.029

0.057

0.057

0.029

0.029

S22

0.029

0.029

0.029

0.057

0.029

0.000

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.057

0.057

0.057

0.057

0.057

0.057

S31

0.029

0.057

0.057

0.057

0.057

0.029

0.057

0.057

0.057

0.057

0.057

0.057

0.086

0.057

0.057

0.057

0.029

0.029

0.029

S32

0.029

0.029

0.029

0.029

0.057

0.057

0.057

0.000

0.029

0.029

0.029

0.057

0.086

0.029

0.029

0.057

0.057

0.029

0.029

S33

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.029

0.000

0.029

0.029

0.057

0.086

0.029

0.029

0.029

0.029

0.029

0.029

S41

0.029

0.029

0.029

0.057

0.057

0.057

0.057

0.057

0.057

0.057

0.057

0.057

0.086

0.057

0.086

0.029

0.029

0.029

0.029

S42

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.029

0.029

0.057

0.029

0.057

0.086

0.057

0.057

0.029

0.029

0.029

0.029

S43

0.029

0.029

0.029

0.000

0.057

0.057

0.029

0.057

0.057

0.057

0.057

0.029

0.114

0.057

0.057

0.057

0.029

0.029

0.029

S44

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.086

0.057

0.086

0.057

0.114

0.000

0.057

0.057

0.057

0.029

0.029

0.029

S51

0.029

0.029

0.029

0.057

0.057

0.057

0.057

0.057

0.029

0.057

0.057

0.057

0.057

0.029

0.086

0.057

0.057

0.029

0.029

S52

0.029

0.029

0.057

0.029

0.057

0.057

0.057

0.057

0.029

0.057

0.057

0.057

0.057

0.057

0.029

0.057

0.057

0.057

0.057

S53

0.057

0.029

0.029

0.029

0.057

0.057

0.057

0.057

0.057

0.057

0.057

0.029

0.086

0.029

0.029

0.029

0.057

0.057

0.057

S54

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.057

0.057

0.029

0.029

0.029

S61

0.000

0.000

0.000

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.000

0.029

S62

0.000

0.000

0.000

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.029

0.000

Normalized matrix N for sub-criteria

Computing the total relation matrix

As previously explained total relation matrix will acquire with following formula:

S11

S12

S13

S14

S21

S22

S31

S32

S33

S41

S42

S43

S44

S51

S52

S53

S54

S61

S62

S11

0.065

0.095

0.104

0.139

0.173

0.169

0.119

0.125

0.113

0.162

0.119

0.125

0.178

0.125

0.136

0.132

0.124

0.076

0.076

S12

0.098

0.101

0.138

0.120

0.184

0.180

0.158

0.134

0.121

0.170

0.128

0.133

0.164

0.134

0.146

0.142

0.133

0.110

0.110

S13

0.082

0.085

0.065

0.101

0.155

0.151

0.135

0.110

0.100

0.089

0.105

0.082

0.132

0.110

0.118

0.118

0.111

0.093

0.093

S14

0.091

0.093

0.102

0.112

0.171

0.168

0.119

0.122

0.111

0.159

0.117

0.094

0.148

0.123

0.135

0.131

0.152

0.103

0.103

S21

0.073

0.073

0.106

0.086

0.082

0.108

0.066

0.093

0.085

0.070

0.062

0.063

0.084

0.092

0.100

0.128

0.124

0.081

0.081

S22

0.100

0.101

0.111

0.150

0.162

0.130

0.134

0.138

0.124

0.148

0.132

0.137

0.169

0.164

0.177

0.173

0.165

0.141

0.141

S31

0.131

0.163

0.176

0.188

0.246

0.212

0.206

0.213

0.193

0.227

0.204

0.215

0.286

0.211

0.228

0.223

0.181

0.148

0.148

S32

0.106

0.109

0.119

0.128

0.198

0.194

0.167

0.121

0.133

0.157

0.140

0.176

0.234

0.146

0.159

0.184

0.172

0.120

0.120

S33

0.096

0.098

0.107

0.115

0.180

0.177

0.125

0.133

0.092

0.141

0.126

0.162

0.215

0.132

0.143

0.141

0.130

0.108

0.108

S41

0.128

0.132

0.146

0.186

0.241

0.235

0.201

0.211

0.190

0.224

0.202

0.214

0.282

0.209

0.254

0.193

0.179

0.146

0.146

S42

0.110

0.112

0.123

0.134

0.206

0.202

0.145

0.155

0.138

0.193

0.147

0.184

0.243

0.181

0.196

0.163

0.150

0.124

0.124

S43

0.120

0.122

0.134

0.118

0.224

0.220

0.160

0.198

0.179

0.209

0.189

0.175

0.292

0.196

0.212

0.207

0.165

0.136

0.136

S44

0.125

0.128

0.140

0.151

0.234

0.229

0.169

0.230

0.185

0.243

0.196

0.260

0.199

0.203

0.220

0.214

0.173

0.142

0.142

S51

0.125

0.128

0.142

0.181

0.234

0.228

0.196

0.204

0.157

0.217

0.196

0.205

0.247

0.175

0.247

0.215

0.202

0.143

0.143

S52

0.124

0.127

0.167

0.153

0.233

0.228

0.197

0.203

0.158

0.215

0.195

0.204

0.246

0.202

0.191

0.214

0.201

0.170

0.170

S53

0.147

0.123

0.135

0.149

0.226

0.221

0.189

0.197

0.180

0.210

0.188

0.173

0.265

0.168

0.184

0.179

0.194

0.164

0.164

S54

0.096

0.097

0.107

0.115

0.179

0.175

0.125

0.130

0.117

0.138

0.124

0.129

0.158

0.129

0.168

0.166

0.130

0.109

0.109

S61

0.046

0.047

0.053

0.087

0.112

0.110

0.094

0.098

0.089

0.104

0.095

0.100

0.120

0.098

0.106

0.104

0.098

0.055

0.083

S62

0.046

0.047

0.053

0.087

0.112

0.110

0.094

0.098

0.089

0.104

0.095

0.100

0.120

0.098

0.106

0.104

0.098

0.083

0.055

Total relation matrix T for sub-criteria

Obtaining the impact-relations-map

In order to determine impact-relation-map, threshold value must be calculated as explained in previous part. With this technique slight relation can be skipped. In this part, threshold value has been calculated equal to 0.147. As long as the threshold value has been calculated, the final result can be shown in an IRM demonstrated below:

S11

S12

S13

S14

S21

S22

S31

S32

S33

S41

S42

S43

S44

S51

S52

S53

S54

S61

S62

S11

0.173

0.169

0.162

0.178

S12

0.184

0.180

0.158

0.170

0.164

S13

0.155

0.151

S14

0.171

0.168

0.159

0.148

0.152

S21

S22

0.150

0.162

0.148

0.169

0.164

0.177

0.173

0.165

S31

0.163

0.176

0.188

0.246

0.212

0.213

0.193

0.227

0.204

0.215

0.286

0.211

0.228

0.223

0.181

0.148

0.148

S32

0.198

0.194

0.167

0.157

0.176

0.234

0.159

0.184

0.172

S33

0.180

0.177

0.125

0.162

0.215

S41

0.186

0.241

0.235

0.201

0.211

0.190

0.202

0.214

0.282

0.209

0.254

0.193

0.179

S42

0.206

0.202

0.155

0.193

0.184

0.243

0.181

0.196

0.163

0.150

S43

0.224

0.220

0.160

0.198

0.179

0.209

0.189

0.292

0.196

0.212

0.207

0.165

S44

0.151

0.234

0.229

0.169

0.230

0.185

0.243

0.196

0.260

0.203

0.220

0.214

0.173

S51

0.181

0.234

0.228

0.196

0.204

0.157

0.217

0.196

0.205

0.247

0.247

0.215

0.202

S52

0.167

0.153

0.233

0.228

0.197

0.203

0.158

0.215

0.195

0.204

0.246

0.202

0.214

0.201

0.170

0.170

S53

0.147

0.149

0.226

0.221

0.189

0.197

0.180

0.210

0.188

0.173

0.265

0.168

0.184

0.194

0.164

0.164

S54

0.179

0.175

0.158

0.168

0.166

S61

S62

IRM for sub-criteria

In regard to IRM for sub-criteria causal relation diagram is produced as below:

Sub Criteria

D

R

D+R

D-R

Awareness/Visibility

2.355

1.911

4.267

0.444

Flexibility

2.602

1.985

4.588

0.617

Adaptability

2.034

2.229

4.263

-0.195

Capacity/Elasticity

2.353

2.499

4.853

-0.146

Acquisition

1.657

3.552

5.208

-1.895

On-Going

2.696

3.446

6.143

-0.750

Provider

3.800

2.800

6.599

1.000

Compliance

2.885

2.914

5.799

-0.029

HR

2.531

2.556

5.086

-0.025

Physical & Environmental

3.720

3.179

6.899

0.540

Communication & Operation

3.029

2.759

5.788

0.269

Access Control

3.393

2.931

6.323

0.462

Data

3.587

3.781

7.368

-0.195

Serviceability

3.584

2.894

6.479

0.690

Availability

3.598

3.226

6.824

0.371

Functionality

3.455

3.132

6.587

0.323

Effectiveness

2.502

2.881

5.384

-0.379

Function #1

1.700

2.252

3.952

-0.552

Function #n

1.700

2.252

3.952

-0.552

Causal diagram for sub-criteria

The sum of indices in each row (D) as previously explained denotes degree of effect, given by that criterion on other criteria in the system. In this case Provider sub-criterion has the most effect given. After that Acquisition, Function#1 and Function#n with approximately equivalent weight have the lowest effect given.

The sum of each column (R) as previously explained denotes degree of effect, received by that criterion on other criteria in the system. Base on this Data and Acquisition have the most effect received by other criteria. Awareness/Visibility and Flexibility criteria have the lowest effect received from other criterion.

In this part, in the horizontal axis vector (D + R) base on calculated results Physical & Environmental and Availability sub-criteria having the most interaction with other sub-criteria that are covered.

For the vertical axis vector (D – R) positive values represent that particular sub-criterion is a net causer. For negative values, that particular sub-criterion is a net receiver (Tzeng et al. 2007; Tamura et al., 2002).

Output of DEMATEL Scatter graph for sub-criteria

The final criteria’s priority by ANP technique

Calculation of unweighted super-matrix, weighted super-matrix aand limit super-matrix

To reach the entire priorities in a system with mutual effect, internal priority vectors (calculated W’s) must be inserted in the proper column of a matrix. As a result, a supermatrix (partitioned matrix) will be acquire, which demonstrates relations between clusters in the system. In other words, a super-matrix is a matrix of relation between network elements, which is calculated base on priority vectors of those relations. This matrix formulates a framework for determining relative importance of criteria after all pairwise comparisons. In consideration of determined relation in this research, the super-matrix is as below:

0 0 0

W21 W22 0

0 W32 W33

Goal

Main criteria

Sub-criteria

W=

Structure of initial unweighted super-matrix

In this super-matrix:

Vector W21 represents the effect of goal on each main criteria.

Vector W22 represents the Main Criteria interdependencies’ Pairwise Comparison.

Vector W32 represents the effect of each main criterion on each sub-criterion.

Vector W33 represents the Sub-criteria interdependencies’ pairwise comparison.

The 0 indices represent the affectless of criteria in that particular place.

As a result of performed calculation, the initial unweighted super-matrix is demonstrated in below figure:

Initial unweighted supermatrix

With using normalization concept, unweighted super-matrix is converted to weighted super-matrix (normal). In weighted super-matrix, sum of all indices of all column is equal to 1.

Weighted supermatrix

In the next step, limit supermatrix is calculated. Limit supermatrix is calculated by repeating exponentiation until all indices of supermatrix get closer to each other. In this situation all indices will be equal to 0 and only those indices related to sub-criteria will be a number that repeats in all rows of those particular sub-criteria. The calculated limid supermatrix by Super Decision software is illustrated below:

Limit supermatrix

At last and base on calculation performed by Super Decision software, the output for final priority of criteria and sub-criteria is illustrated below:

Sub Criteria

Total

Normal

Ideal

Ranking

S11

0.0191

0.0191

0.1535

15

S12

0.0329

0.0329

0.2648

12

S13

0.0037

0.0037

0.0295

17

S14

0.0213

0.0213

0.1713

14

S21

0.0106

0.0106

0.0854

16

S22

0.0446

0.0446

0.3593

10

S31

0.1242

0.1242

1

1

S32

0.0564

0.0564

0.4544

9

S33

0.035

0.035

0.2815

11

S41

0.089

0.089

0.7163

5

S42

0.0762

0.0762

0.6132

8

S43

0.0835

0.0835

0.6724

7

S44

0.0901

0.0901

0.7251

4

S51

0.0854

0.0854

0.6871

6

S52

0.1014

0.1014

0.8166

2

S53

0.099

0.099

0.7969

3

S54

0.0218

0.0218

0.1758

13

S61

0.0029

0.0029

0.0235

18

S62

0.0029

0.0029

0.0235

19

The final priority of all factors in the model by ANP

the chart for final priority of all factors in the model by ANP

The results obtained from weights of factors in above figure can be used as management dashboard.