## 4 Case Study
### Evaluating and Ranking of Suppliers
#### 4.2.1 Criteria Used  
Resilience Capability Criteria: Operational capabilities of the suppliers that affect the interconnected firms' resilience performance (_resilience value_\(=f(\mu_{r})\)). In previous literature, the measurement of SC resilience has been operationalized using two approaches: (1) subjective measures of SC capabilities that enable resilience performance [19; 21], and (2) objective measures of capacities such as absorptive, adaptive, and restorative capacities, which are summed to provide an overall measure of the resilience performance [79; 80]. However, [PERSON] et al. [81] emphasized that the performance measurement model and its accuracy were insignificant unless supplemented with an applicable planning policy. Hence, this study focuses on adopting and operationalizing subjective resilience attributes to stay within the study's scope of developing a resilience-based management policy. * Flexibility [C1, \(f(\mu_{\text{i1}})\)]: Flexibility is the degree of easiness in managing alternatives under environmental and operational uncertainties [45; 61] (i.e., how easily can SCs change its volume and process?) * Agility [C2, \(f(\mu_{\text{i2}})\)]: Ability is the timeliness in managing alternatives and system reconfiguration to sudden changes in supply and demand [41; 82] (i.e., how fast can SCs respond and adapt?) Figure 1: Network structure of the evaluated case. * Efficiency [C3, \(f(\mu_{i3})\)]: Efficiency is the level of resources utilized for the derived operational results [83] (i.e., how easily can SCs control resources while managing lean management practices?) * Alertness [C4, \(f(\mu_{i4})\)]: Alertness the degree of readiness in dealing with environmental and operational risks and emergencies [84] (i.e., how fast can SCs detect disruptive events?) To determine a single supplier \(i\)'s overall resilience value, the resilience value of a node \(i\), \(\mu_{i}\), is measured by the weighted sum of the resilience capabilities of supplier \(i\), where \(k_{ir}\) represents the weight of capability criteria \(r\). The degree of each resilience capability \(r\) for firm \(i\) is determined by the linguistic scale of firm's experts with the following scales: \(0=\) nonexistent, \(1=\) very low capability, \(3=\) low capability, \(5=\) average capability, \(7=\) high capability, \(9=\) very high capability, \(10=\) maximal capability. \[\mu_{i}=\sum_{r=1}k_{ir}\mu_{ir}\ \forall i \tag{9}\]  
Network Criteria: Network characteristics that enable effective sourcing and/or rerouting options in disruptive events (_network value_\(=f(\gamma_{i})\)). Among various network attributes, this study is mainly interested in the degree of centrality and betweenness centrality as proposed by [PERSON] et al. [85] for the following reasons. First, most real-world network structures follow a scale-free model whose properties depend on the characteristics of the nodes [86]. Specifically, a scale-free model follows a power law distribution with a certain value of degree exponent that includes the growth rate of the node's degree with respect to the network size. In practice, this is very useful, as one can foresee whether a centralized (winner-takes-all) structure may eventually convert to a hub-and-spoke structure. Second, other metrics are temporarily disregarded as their validity relies heavily on complete and accurate information on the network system. The following measures of network characteristics (\(t\)) at the node level are adopted for the measurement model. * Degree of centrality [C5, \(f(\gamma_{i1})\)]: The degree centrality of a node \(i\), \(\gamma_{i1}\), is measured by the number of direct links that are connected to node \(i\). \(x_{ij}\) takes a binary value of \(1\) if there is a link between nodes \(i\) and \(j\), and \(0\) otherwise. \[\gamma_{i1}=\sum_{j=1}x_{ij}=\sum_{j=1}x_{ji}\ \forall i\] (10)
* Betweenness centrality [C6, \(f(\gamma_{i2})\)]: The betweenness centrality of a node \(i\), \(\gamma_{i2}\), is measured by the total number of links that contain node \(i\).