## 3 Algorithm
There are 8 travel time upper bound vectors that are shown in \[v_{3}+v_{5} \leq 80,\]2 The time reliability \(R_{120}\) in an SCCNMT according to Table 5 using the RSDP can be obtained via

\[v_{3}+v_{5} \leq 80,\]3

## 5 Discussion and Conclusions

Network reliability can be used as a performance indicator that indicates the SCCNMT's ability of successfully meeting the demands of retailers and delivering within time constraints. This performance indicator can provide logistics companies with a decision-making basis for determining transportation routes and vehicle configurations, and can also be used for sensitivity analysis to identify significant transportation routes. Although we consider travel time during transportation, only travel data on highways are available from public data. To be more comprehensive, we need travel time data on both highways and surface roads for more realistic and accurate performance indicators. \begin{table}
\begin{tabular}{c} \hline \hline
**Step 2.2** \\
**Travel Time Vector** \\ \hline \(S_{1}\) = (35, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \(S_{2}\) = (40, 45, 35, 35, 40, 45, 30, 30, 40, 40) \\ \(S_{3}\) = (45, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \(S_{4}\) = (35, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \(S_{5}\) = (40, 45, 35, 35, 45, 40, 30, 30, 40, 40) \\ \(S_{6}\) = (45, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \(S_{7}\) = (45, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \(S_{8}\) = (45, 45, 35, 35, 45, 45, 30, 30, 40, 40) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The results for a numerical example. In this article, we introduce a SCC model, which models the entire product chain and calculates network reliability using stochastic flow. Additionally, because travel time is a crucial factor in a cold chain network, we need to consider it as an additional factor by calculating time reliability and multiplying it with the multi-state flow to estimate network reliability. This way, we can evaluate network reliability not only by including multi-state flow but also considering the multi-state travel time. Currently, this research only considers a single product in a cold chain network, but in the future, it can be extended to study the inventory service and multiple commodities. The authors contributed equally to the work. All authors have read and agreed to the published version of the manuscript. National Science and Technology Council Taiwan: 109-2221-E-009-067-MY3 and 111-2221-E-167-010. The data used can be obtained from the references cited. The authors declare



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