## 3 The Proposed Framework  
In this section, the bicriterion network resilience (BNR) model is proposed to compute and visualize the resilience and network relations between firms. An ordering approach, concordance and discordance, is then applied to determine firms' priorities for enhancing the overall supply network resilience. The ultimate goal of network representation is to help practitioners maintain a prescribed balance among firms. In doing so, a confidence level on supplier network resilience performance can be justified. Each step of the network resilience priority assessment is detailed as in the following.  
**Step 1.** Identifying potential suppliers for the network under investigation  
As the first step of the proposed framework, a supply network manager or a committee consisting more than one manager must identify involved or key suppliers for the orders and products under investigation. Then \(N\) is treated as a a finite set of supply network connected firms (nodes).  
**Step 2.** Identifying appropriate resilience and network criteria for supplier evaluation  
Appropriate evaluation criteria must be determined prior to supply network evaluation. Aligned with [PERSON]'s [74] suggestion, primary criteria are developed based on literature review which is then validated by the company's expert for a final criterion. As a comprehensive list of resilience capabilities, various capabilities have been identified: collaboration, agility, alertness, information sharing, risk control, trust [75]; collaboration, flexibility, agility, visibility, velocity, redundancy, robustness, rapidity, responsiveness [48], situation awareness, robustness, knowledge management, security, visibility, flexibility, redundancy, collaboration, agility, contingency planning, market position, social capital [3]; flexibility, redundancy, agility, collaboration, information sharing, visibility [44]; flexibility, velocity, visibility [45]. On the contrary, only limited network attributes have been operationalized as network criteria for supplier.  
Then we let \(C\) represent a finite set of criteria of a firm's value with given ordinal measurement scales and \(k\) be an criteria weight vector such that \(k(c)>0\) for all \(c\in C\). For each supply network connected firm, \(n\), evaluate \(c\) criteria based on the resilience and network attributes (\(\mu,\ \gamma\)) and the corresponding weights \(k(c)\).  
**Step 3.** Determining the values of the criteria using linguistic and network assessment For the evaluation of capability criteria, this study adopts a probabilistic approach which can effectively utilize empirical data. Based on the empirical data, a normal probability distribution is formed for each criterion, and thus, the probability that node \(n_{i}\) is true can be expressed as firm \(i\) resilience attribute \(\mu\) with a value of \(\varphi\). As the node's resilience capability is measured using the SC capabilities, the individual firm's resilience likelihood can be estimated.  
\[\begin{split} P(n_{i})=\textit{survival likelihood of node $n_{i}$ in case of a disruption}\\ =Pr(\mu_{ir}\leq\varphi_{ir})\ \forall i\end{split} \tag{1}\]  
The evaluation of network criteria is determined based on various quantitative measurements of network attributes include the average degree, network diameter, network centralization, network heterogeneity, degree exponent, and assortativity [76].