# Supply-Demand Dynamic Matching in Cloud Manufacturing Based on Hypernetwork Model
## 4 Dynamic Matching Method
### Specific Mechanism of Rematching
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Index**} & \multicolumn{3}{c}{**20:100**} & \multicolumn{3}{c}{**40:100**} & \multicolumn{3}{c}{**60:100**} & \multicolumn{3}{c}{**80:100**} \\ \cline{3-10}  & & **OPE** & **OPE-NR** & **OPE** & **OPE-NR** & **OPE** & **OPE-NR** & **OPE** & **OPE-NR** \\ \hline \multirow{3}{*}{t} & M & 0.394 & 0.331 & 0.6 & 0.543 & 1.093 & 1.020 & 1.288 & 1.094 \\  & SD & 0.067 & 0.043 & 0.075 & 0.036 & 0.085 & 0.072 & 0.199 & 0.128 \\  & P & \textless{}0.001 & & \textless{}0.001 & & \textless{}0.001 & & \textless{}0.001 \\ \hline \multirow{3}{*}{u} & M & 264.0 & 277.1 & 513.5 & 528 & 777.6 & 798.1 & 1042.4 & 1064.3 \\  & SD & 20.4 & 17.1 & 24.5 & 22.6 & 35.5 & 30.4 & 39 & 42 \\  & P & 0.002 & & 0.009 & & 0.007 & & 0.006 \\ \hline \multirow{3}{*}{c} & M & 0.571 & 0.584 & 0.567 & 0.576 & 0.574 & 0.583 & 0.534 & 0.541 \\  & SD & 0.014 & 0.014 & 0.017 & 0.014 & 0.011 & 0.009 & 0.014 & 0.149 \\  & P & \textless{}0.001 & & 0.009 & & 0.001 & & 0.014 \\ \hline \multirow{3}{*}{l} & M & 596.8 & 534.1 & 1539 & 1408 & 2519 & 2187 & 3123 & 2839 \\  & SD & 58.1 & 40.3 & 95 & 86.1 & 234 & 271 & 358 & 333 \\ \cline{1-1}  & P & 0.04 & & 0.008 & & \textless{}0.001 & & 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Rematching data in multiple scenarios. Figure 6: Comparison of methods with and without considering network resilience. (**a**) The comparison of the rematching time. (**b**) The comparison of the operation utility. results in better network connectivity after rematching. However, at the task service ratio of 80:100, the average clustering coefficient decreases. This is because, as the number of tasks increases to a certain extent and service resources become scarce, more service nodes with fewer neighboring connections are involved, potentially reducing the average connections and, consequently, lowering the clustering coefficient of the nodes. Finally, a comparison of load balance is presented in Figure 7b. The results demonstrate that the matching scheme that considers the network generally leads to better load distribution in response to dynamic situations. As the number of tasks increases, load imbalance variance gradually increases due to the scarcity of service resources and repetitive use of the same services, concentrating load on specific nodes. A more balanced network load implies that in the face of future dynamic disruptions, the failure of individual nodes is less likely to cause irreparable damage to the entire network. Therefore, through a comparative analysis of different task service ratios, some management recommendations for manufacturing systems can be proposed. To enhance the resilience and adaptability of a manufacturing system within a dynamic environment, it is crucial to continuously monitor the relationship between the number of tasks and available services in real time. When service resources are more abundant, the system exhibits greater elasticity. However, an excessive surplus of resources may result in inefficiencies and waste. Thus, further investigation into the optimal ratio of tasks and services is necessary to determine the most balanced system dynamic response capability. #### 5.2.4 The Sensitivity Analysis of Parameters

In this section, a sensitivity analysis of the model parameters was conducted by slightly adjusting the values of the parameters to observe how the output results change. Given the large number of nodes in the model, with each service and task node having its own set of parameters, certain simplifications were made by grouping related parameters together. For example, the unit cost of service \(i\) is denoted as \(C_{\mathrm{S}}^{i}\in[0.1,1]\), and all \(C_{\mathrm{S}}^{i}\) values were aggregated into a parameter group \(C_{\mathrm{S}}=\left\{C_{\mathrm{S}}^{i}|i=1,2,...,NoS\right\}\), with the analysis focusing on how the overall variation of \(C_{\mathrm{S}}\) influences the model results.