# Supply-Demand Dynamic Matching in Cloud Manufacturing Based on Hypernetwork Model
## 3 Modeling of the SDM Problem Based on the Hypernetwork Model
### Initial Matching Model
#### 3.3.2 Operational Indicator Modeling  
(1) Utility of service providers  
In addition to evaluating the network topology, the operational utility of platform participants is also considered. The utility assessment focuses separately on service providers and task requesters. For service providers, three aspects of utility are considered: revenue, time consistency, and reliability from allocated manufacturing tasks. Reverue refers to the difference between the expense offered by task \(j\) and the service cost, which is expressed as Equation (20). \[E^{S}=\sum_{i=1}^{NoS}\sum_{j=1}^{NoT}(x_{ij}*(C_{T}^{j}-C_{S}^{i}*B_{T}^{j})). \tag{20}\]  
Time consistency accounts for the waste of service time resources, specifically the overlap between task time and available service time, which is formulated as Equation (21). \[T^{S}=\sum_{i=1}^{NoS}\sum_{j=1}^{NoT}(x_{ij}*((Et_{S}^{i}-St_{S}^{i})-(Et_{T} ^{j}-St_{T}^{j}))). \tag{21}\]Reliability reflects the likelihood of order variations, measured using the reputation of the demand side, calculated by Equation (22). \[TR^{S}=\sum_{i=1}^{NoS}\sum_{j=1}^{NoT}(x_{ij}*\eta_{T}^{j}). \tag{22}\]  
Evaluation indicators are defined using multi-attribute utility theory [45]. Revenue and reliability are positively correlated indicators, meaning they are directly proportional to utility. Time consistency is a negatively correlated indicator, with a smaller value indicating a better match between available service time and the required task time; it reflects a higher proportion of task scheduling within the service's available time. The service utility function is shown in Equation (23). \[U_{S}=\omega_{e}^{S}U_{E}^{S}+\omega_{t}^{S}U_{T}^{S}+\omega_{r}^{ S}U_{R}^{S}\] \[=\omega_{e}^{S}*\gamma_{e}E^{S}+\omega_{t}^{S}*\gamma_{t}T^{S}+ \omega_{r}^{S}*TR^{S}, \tag{23}\]  
where \(U_{E}^{S}\), \(U_{T}^{S}\), and \(U_{R}^{S}\) represent revenue utility, time utility, and reliability utility, \(\omega_{e}^{S}\), \(\omega_{t}^{S}\), and \(\omega_{r}^{S}\) represent the utility preference weights, respectively. To standardise and unify the scales of various utility values, scaling factors \(\gamma_{e}\) and \(\gamma_{t}\) are introduced. Since time consistency is a negatively correlated indicator, we have \(\gamma_{t}<0\). 1. Utility of task requesters  
For task requesters, three utility aspects are considered: total manufacturing cost, service quality, and reliability. Total cost represents the expenses for selecting services, which can be calculated by Equation (24). \[C^{T}=\sum_{j=1}^{NoT}\sum_{i=1}^{NoS}(x_{ij}*C_{S}^{i}*B_{T}^{j}). \tag{24}\]  
Service quality denotes the quality that the services can provide, as calculated by Equation (25). \[Q^{T}=\sum_{j=1}^{NoT}\sum_{i=1}^{NoS}(x_{ij}*Q_{S}^{i}). \tag{25}\]  
Reliability is considered in terms of the likelihood of service failure, which is measured by the reputation of the service providers, calculated by Equation (26). \[TR^{T}=\sum_{j=1}^{NoT}\sum_{i=1}^{NoS}(x_{ij}*\eta_{S}^{j}). \tag{26}\]  
In this context, cost is a negatively correlated indicator, meaning a higher numerical value indicates poorer utility, while service quality and reliability are both positively correlated indicators. The task utility function is defined by Equation (27). \[U_{T}=\omega_{c}^{T}U_{C}^{T}+\omega_{q}^{T}U_{Q}^{T}+\omega_{r}^ {T}U_{R}^{T}\] \[=\omega_{c}^{T}*\gamma_{c}C^{T}+\omega_{q}^{T}*\gamma_{t}Q^{T}+ \omega_{r}^{T}*TR^{T}, \tag{27}\]  
where \(U_{C}^{T}\), \(U_{Q}^{T}\), and \(U_{R}^{T}\) denote cost utility, quality utility, and reliability utility, \(\omega_{c}^{T}\), \(\omega_{q}^{T}\), and \(\omega_{r}^{T}\) are the utility preference weights, respectively. \(\gamma_{c}\), \(\gamma_{q}\) are the corresponding scaling factors for standardising the data. Since \(C^{T}\) is negatively correlated with \(U_{T}\), we have \(\gamma_{c}<0\). The comprehensive operational utility \(U_{2}\) is obtained by aggregating the utilities of both service providers and task requesters, as expressed by Equation (28).