# PSO-SVM Based Performance-Driving Scheduling Method for Semiconductor Manufacturing Systems
## 3 Framework of the Proposed Scheduling Method
### Composite Dispatching Rules (CDR)  
CDR considers the characteristics related to process constraints, such as the intervals between two successive workpieces, the processing time of workpieces, and the processing sequence. In addition, to better prioritize workpiece dispatching and equipment maintenance, CDR considers the characteristics related to equipment maintenance and workpiece dispatching, such as workload of downstream equipment, index of equipment maintenance, and due date of workpiece processing. A flowchart of CDR is illustrated in Figure 2.  
Step 1: Check whether workpiece \(j\) satisfies the process constraint \(G_{j,C}^{c}<\left(H_{C}-T_{j}^{C}\right)\), where \(G_{j,C}^{c}\) represents the total remaining processing time of constraint \(C\), \(H_{C}\) represents the time constraint of \(C\), and \(T_{j}^{C}\) represents the processing completion time of workpiece \(j\) in constraint \(C\). Step 2: Compute the index (\(P_{1}\)) of process constraints:  
\[P_{1}=\left\{ \begin{array}{cc}P_{MAX},&G_{j,C}^{c}\times\Omega\geq H_{C}-T_{ n}^{C}\\ \frac{G_{j,C}^{c}\times\Omega}{H_{C}-T_{n}^{C}},&G_{j,C}^{c}\times\Omega<H_{C}- T_{n}^{C}\end{array} \right., \tag{1}\]  
where \(\Omega\) is a constant that can be obtained from the manufacturing execution system. This implies that, for workpiece \(j\), which is subjected to process constraint \(C\), the greater the ratio of \(G_{j,C}^{c}\) to \(H_{C}-T_{n}^{C}\) the higher the probability of workpiece \(j\) violating constraint \(C\), and the higher priority of workpiece \(j\) to be selected and processed on equipment \(i\). If \(\left(G_{j,C}^{c}\times\Omega\right)\geq\left(H_{C}-T_{n}^{C}\right)\), workpiece \(j\) will have a greater probability of  
Figure 2: Flowchart of CDR. violating constraint \(C\) and become a hot lot, i.e., it will have the highest priority (\(P_{MAX}=1\)) on any equipment. Step 3: Compute the index of the due date (\(P_{3}\)) for workpiece \(j\)  
\[P_{3}=t_{j}^{r_{p}}/\left(t_{j}^{D}-t\right) \tag{2}\]  
where \(t_{j}^{r_{p}}\) represents the remaining processing time of workpiece \(j\), \(t_{j}^{r_{p}}\) represents the due date of workpiece \(j\), and \(t\) r represents the current decision time. Step 4: Compute the workpiece priority (\(P_{LOT}\)):  
\[P_{LOT}=\sum_{n=1}^{3}(\alpha_{n}\cdot P_{n}) \tag{3}\]  
where \(\alpha_{n},n\in\{1,2,3\}\) r represents the nth parameter of \(P_{LOT}P_{1}\) is the index of process constraints, \(P_{2}\) is an inherent index (1, 4) of customer priority, and \(P_{3}\) is the index of due date. Step 5: Check whether the current decision time is within the equipment maintenance period:  
\[\left\{ \begin{array}{c}t-t_{M}^{E}\geq 0.\\ t_{M}^{L}-t\geq t_{M}^{MAX}\end{array} \right. \tag{4}\]  
where \(t_{M}^{E}\) and \(t_{M}^{L}\) respectively represent the earliest start time and latest end time of equipment maintenance; \(t_{M}^{MAX}\) represents the maximum maintenance time. If the current decision time is within the equipment maintenance period, go to Step 6; otherwise, dispatch workpieces according to \(P_{LOT}\). Step 6: Compute the index of equipment maintenance (\(P_{4}\)):  
\[P_{4}=t_{M}^{MAX}/\left(t_{M}^{L}-t\right) \tag{5}\]  
Step 7: Compute the index of workload (\(P_{5}\)) for downstream equipment:  
\[P_{5}=\sum t_{j}^{i+1}/t_{i+1}^{a} \tag{6}\]  
where \(t_{j}^{i+1}\) represents the waiting and processing time of workpiece \(j\) non-downstream equipment; \(t_{i+1}^{a}\) represents the daily available time of downstream equipment. Clearly, if \(t_{i}^{n}(t)\geq 1\), the workload of the downstream equipment will exceed its daily available time; that is, the equipment will become a bottleneck. If there exist several pieces of equipment that complete the same process, \(t_{i+1}^{a}\) represents the available processing time of all of them. Step 8: Compute the maintenance priority (\(P_{PM}\)):  
\[P_{PM}=\sum_{n=4}^{5}(\alpha_{n}\cdot P_{n}) \tag{7}\]  
Step 9: Normalize the workpiece priority (\(P_{LOT}\)) and maintenance priority (\(P_{PM}\)).