## 4 Case Study
### Evaluating and Ranking of Suppliers
#### 4.2.2 Ranking of Suppliers  
Each node is evaluated based on four capabilities (\(\mu_{i1},\ \mu_{i2},\ \mu_{i3},\ \mu_{i4}\)) and network attributes (\(\gamma_{i1},\ \gamma_{i2}\)) on a scale ranging from \(0\) to \(10\). In this case, a prior information matrix is formed, as presented in Table 1, with weights that can be obtained by a group of experts' linguistic assessment illustrated in Section 4.2.1. For example, the average evaluation of flexibility capability (\(r=1\)) for firm 1 is 9 representing a very high degree of firm's ability to change its volume and process. While firm 15 has the lowest degree of centrality (\(k=1\)) with value of 0, firms 1, 2, 3, 4, 6, and 7 have highest degree of centrality with value of 8.89. High degree of centrality and betweenness centrality reflect the significant network value in creating a complexity within the SC network. As a base case scenario, equal weights are computed, and the average weighted performances of the attributes are also listed in the table. For each node, S-count (\(S_{c}(i)\)) and I-count (\(I_{c}(i)\)) are computed to represent how superior or inferior a node is to other nodes in the network. Based on the comparison of \(S_{c}(i)\) and \(I_{c}(i)\), the attributes that belong to the concordance (C) and the discordance (D) sets are indicated in the R-columns of Table 2. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline
**Supplier (\(i\))** & **C1 (\(\mu_{i1}\))** & **C2 (\(\mu_{i2}\))** & **C3 (\(\mu_{i3}\))** & **C4 (\(\mu_{i4}\))** & **C5 (\(\
u_{i1}\))** & **C6 (\(\
u_{i2}\))** & **Weighted Average** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 1: Prior rating information matrix of L Electronics’ connected nodes. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline  & & & & & & & & & & & & & & & & & & & \\ \multicolumn{12}{c}{**Resilience Values**} & \multicolumn{1}{c}{**Network Values**} \\ \multicolumn{12}{c}{} & \multicolumn{1}{c}{**C1 (\(\mu_{i1}\))**} & \multicolumn{1}{c}{**C2 (\(\mu_{i2}\))**} & \multicolumn{1}{c}{**C3 (\(\mu_{i3}\))**} & \multicolumn{1}{c}{**C4 (\(\mu_{i4}\))**} & \multicolumn{1}{c}{**C5 (\(\
u_{i1}\))**} & \multicolumn{1}{c}{**C6 (\(\
u_{i2}\))**} \\ \hline Supplier & \multirow{2}{*}{\(S_{1}\)} & \multirow{2}{*}{I\({}_{1}\)} & \multirow{2}{*}{R\({}_{1}\)} & \multirow{2}{*}{S\({}_{2}\)} & \multirow{2}{*}{I\({}_{2}\)} & \multirow{2}{*}{R\({}_{2}\)} & \multirow{2}{*}{S\({}_{3}\)} & \multirow{2}{*}{I\({}_{3}\)} & \multirow{2}{*}{R\({}_{3}\)} & \multirow{2}{*}{S\({}_{4}\)} & \multirow{2}{*}{I\({}_{4}\)} & \multirow{2}{*}{R\({}_{4}\)} & \multirow{2}{*}{S\({}_{5}\)} & \multirow{2}{*}{I\({}_{5}\)} & \multirow{2}{*}{R\(Based on the nodes' rating information, the importance weights (\(\pi^{+},\pi^{-}\)) and preferences (\(\chi^{+},\chi^{-}\)) are presented in Table 3.  
The results show that 10 nodes display extreme discordance levels with respect to concordance levels:  
\[\text{S17}>\text{S16}>\text{S18}>\text{S15}>\text{S12}>\text{S3}>\text{S10}> \text{S19}>\text{S8}>\text{S11}.\]  
Suppliers with high discordance and low concordance levels have significantly negative resilience and network values, thus requiring an improvement in the overall value of the supply network model. The second set of suppliers that need attention are those with similar levels of concordance and discordance. \[\text{S5}>\text{S9}>\text{S2}>\text{S13}>\text{S14}>\text{S7}>\text{S1}>\text{ S6}>\text{S4}.\]  
Although these firms perform better than others on some attributes, they perform worse than others on other attributes. This type of conflicting output creates uncertainty about the level of performance when disruption occurs. Thus, these firms should be carefully monitored and accurately measured in terms of their resilience capabilities and network values. Suppliers with higher concordance values than discordance values are well-balanced firms that are most likely to continue performing in case of disruption.