## 5 Comparison with Interorganizational Workflow under Case Transfer Interoperability
### Calculation of Workflow Performance Indicators in Case Transfer Interoperability  
Taking the above prefabricated building project as an example, the case transfer interorganizational workflow was analyzed based on the Sequential Iteration Model. First, the matrix R for the interorganizational workflow correlation shown in Figure 7 and the time matrix were merged into a DSM matrix, \(M\), which is a Sequential Iteration Design Structure Matrix.  
\[M=\left[\begin{array}{cccc}3&0.133&0&0\\ 0.4536&2&0.167&0.2136\\ 0&0.2331&0.5&0.06\\ 0.06&0.3731&0&1.5\end{array}\right] \tag{28}\]  
Taking the ordering, \"Organization 1, Organization 2, Organization 3, Organization 4\", of workflow sequential iteration as an example, the Markov chain for processing role-based interorganizational workflows can be divided into the following four stages.  
1. Stage 1: intraorganizational workflow processing for Organization 1,
2. Stage 2: transferring to the workflow processing of Organization 2 and performing iterative processing between Organization 2 and Organization 1,
3. Stage 3: transferring to the workflow processing of Organization 3 and performing iterative processing between Organization 3 and Organization 1, and Organization 2,
4. Stage 4: transferring to the workflow processing of Organization 4 and performing iterative processing between Organization 4 and Organization 1, and Organization 2, and Organization 3.  
In the case of transfer interoperability, due to the sequential processing mode among organizations, only one participant organization separately processes the project workflow at any given time. Therefore, the total time taken to complete the workflow processing of each organization in the case of transfer interoperability (\(\Gamma^{*}\)) is the same as the total time spent on the interorganizational workflow process in the case of transfer interoperability (\(\mathrm{E}^{*}\)).  
\[\mathrm{T}^{*}=\mathrm{E}^{*}=T_{1}+T_{2}+T_{3}+T_{4}=3+2.5529+0.9665+2.3798=8.8992 \tag{29}\]  
In the Markov chain of the interorganizational workflow processing, there are \(4\times 3\times 2\times 1=24\) kinds of ordering due to the different iteration sequencing of workflows among organizations. Among the 24 kinds of ordering, there are two kinds of ordering for which \(\mathrm{T}^{*}\) and \(\mathrm{E}^{*}\) are the lowest--namely, the ordering \"Organization 1, Organization 3, Organization 2, Organization 4\" and \"Organization 3, Organization 1, Organization 2, Organization 4.\"  
\[\mathrm{T}^{*}_{\mathrm{min}}=\mathrm{E}^{*}_{\mathrm{min}}=8.6727. \tag{30}\]  
The values of \(\mathrm{T}^{*}\) and \(\mathrm{E}^{*}\) are the largest for the ordering \"Organization 4, Organization 2, Organization 3, and Organization 1.\"  
\[\mathrm{T}^{*}_{\mathrm{max}}=\mathrm{E}^{*}_{\mathrm{max}}=10.1591. \tag{31}\]  
Therefore, for the role-based interorganizational workflow, it is suggested to adopt the ordering \"Organization 1, Organization 3, Organization 2, Organization 4\" or \"Organization 3, Organization 1, Organization 2, Organization 4\" in case of transfer interoperability.