Step 4: Formation of ISM-Based Model
Final reachability matrix and level partition table is used to generate the final
hierarchical structure. All the variables which are at level 1 are placed at the bottom
of the hierarchy and are considered most important and also drives the whole system.
The relationship between factor i and j is denoted by an arrow where direction of the
arrow shows that two factors are related. The resulting graph obtained by
representing the relationship by arrows and level partitioning is known as “directed
graph” or “digraph,” which is also the final hierarchical structure.
3.2 Best-Worst Method
BWM is a very strong MCDM technique and is widely used by researchers all over
the world for decision-making and problem-solving. It is developed by Rezaei
(2015, 2016) and widely used by like Gupta and Barua 2016 (technological innovation enablers ranking); Rezaei et al. 2016 (green supplier selection); Gupta and
Barua 2017 (green supplier selection); Gupta 2018 (airport evaluation based on
service quality); Ahmadi et al. 2017 (social sustainability in supply chains); Zhao
et al. 2018 (benefit evaluation of eco-industrial parks from circular economy and
sustainability perspective); Malek and Desai (sustainable manufacturing barriers
analysis). The steps as given by Rezaei (2015, 2016) are explained below:
Step 1: Selection of criteria (barriers) for analysis.
Through literature review internal barriers to green innovation are finalized.
Step 2: Among finalized criteria best and the worst criteria is chosen by experts.
Step 3: Next each reference ratings on the scale of 1–9 are sought from experts for
best to others and others to worst criteria.
Step 4: Optimized weights (w 1
* , w 2
* , . . .. . . ., w n
* ) for all the criteria is
calculated next.
The objective is to obtain the weights of criteria so that the maximum absolute
differences for all j can be minimized for
w B À a Bj w j
, w j À a jW w W
È
É :
This minimax model will be obtained:
min max w B À a Bj w j
, w j À a jW w W
È
É
s:t:
X
j
w j ¼ 1
w j ! 0, for all j
ð8:1Þ
Model (8.1) is transformed into a linear model; the model is shown below:
146
H. Gupta and M. K. Barua
Final reachability matrix and level partition table is used to generate the final
hierarchical structure. All the variables which are at level 1 are placed at the bottom
of the hierarchy and are considered most important and also drives the whole system.
The relationship between factor i and j is denoted by an arrow where direction of the
arrow shows that two factors are related. The resulting graph obtained by
representing the relationship by arrows and level partitioning is known as “directed
graph” or “digraph,” which is also the final hierarchical structure.
3.2 Best-Worst Method
BWM is a very strong MCDM technique and is widely used by researchers all over
the world for decision-making and problem-solving. It is developed by Rezaei
(2015, 2016) and widely used by like Gupta and Barua 2016 (technological innovation enablers ranking); Rezaei et al. 2016 (green supplier selection); Gupta and
Barua 2017 (green supplier selection); Gupta 2018 (airport evaluation based on
service quality); Ahmadi et al. 2017 (social sustainability in supply chains); Zhao
et al. 2018 (benefit evaluation of eco-industrial parks from circular economy and
sustainability perspective); Malek and Desai (sustainable manufacturing barriers
analysis). The steps as given by Rezaei (2015, 2016) are explained below:
Step 1: Selection of criteria (barriers) for analysis.
Through literature review internal barriers to green innovation are finalized.
Step 2: Among finalized criteria best and the worst criteria is chosen by experts.
Step 3: Next each reference ratings on the scale of 1–9 are sought from experts for
best to others and others to worst criteria.
Step 4: Optimized weights (w 1
* , w 2
* , . . .. . . ., w n
* ) for all the criteria is
calculated next.
The objective is to obtain the weights of criteria so that the maximum absolute
differences for all j can be minimized for
w B À a Bj w j
, w j À a jW w W
È
É :
This minimax model will be obtained:
min max w B À a Bj w j
, w j À a jW w W
È
É
s:t:
X
j
w j ¼ 1
w j ! 0, for all j
ð8:1Þ
Model (8.1) is transformed into a linear model; the model is shown below:
146
H. Gupta and M. K. Barua