## 5 Analysis of Impact of Resource Failures on CPS
As there are two types of products involved in the nominal solution, the algorithm first finds the set \(I(\Delta(m))\) of process types that will be influenced due to the failure. As both types of processes are involved with the use of the failed resointerval, therefore, \(J(\Delta(m))=\{1,2\}\) in Algorithm 3. By solving the FPRSTN defined by \(RSTN_{j}(V_{j},A_{j})\) with residual capacity constraint for \(j=1\), a solution is obtained as follows: \(f_{3,14}=1\), \(f_{14,26}=1\) and \(f_{26,1}=1\). Figure 1(a) shows the above solution represented in \(RSTN_{1}(V_{1},A_{1})\) by rerouting the flows in Figure 1(a). This solution satisfies the condition of Property 3. By solving the FPRSTN defined by \(RSTN_{j}(V_{j},A_{j})\) with residual capacity constraint for \(j=2\), the solution with \(f_{6,18}=1\), \(f_{18,29}=1\) and \(f_{29,40}=1\) in Figure 1(b) is obtained by rerouting the flows in Figure 1(b). The above solution can meet the deadline as the flows of each arc after the deadline is zero and Property 1 holds. Figure 1(a),b show the overall solution obtained by combining the solution (rerouted flows) with the uninfluenced flows for both types of products. The order deadline can be met by this solution as the flows of each arc after the deadline is zero. ## References

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