## 3 Problem Definition and Solution Method
### Current Status of the System
Technicians (machinery) in production have equal skills and conduct the same job in the same time. It is known that the hand tools used by technicians do not make a distinctive difference to the process. This shows that technicians can be considered as identical parallel machines. Each machine (technician) can only do one job at a time. A faulty manufactured card discovered during quality control or functional testing is returned to the production line and must be reprocessed. This process is called \"Rework\". Errors that occur during production due to technician error, material, or equipment problems are noticed during quality control or functional tests after production, and this time increases in direct proportion to the number of components. This information is important as it directly affects the date of return of the card to the system. The release time parameter of the job to be reworked is the sum of the end date of the main job and the quality and testing time of that job. This period can be considered as two units for the number of components between 50 and 100, three units for the number of components between 101 and 150, and four units for the number of components between 151 and 200. The production time of the Rework Card also varies depending on the number of components to be reprocessed. Reprocessing has a distribution function whose production time/number of components ratio can be obtained from historical data. Table 2 (part a) shows the number of components the cards have, the estimated production time based on historical data, and the release date of each card. Table 2 (part b) shows the actual production time of each production and the parameters of the productions that need rework. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{4}{c}{**(a)**} & \multicolumn{6}{c}{**(b)**} \\ \hline \multicolumn{4}{c}{**Parameters**} & \multicolumn{6}{c}{**Realized Parameters**} \\ \hline \multirow{3}{*}{**PCB No**} & \multirow{3}{*}{\begin{tabular}{c} **Component** \\ **Amount** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Release** \\ **Date** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Expected** \\ **Processing** \\ **Time** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **PCB No** \\ **Time** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Re realized** \\ **Processing** \\ **Time** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Rework** \\ **Need?** \\ **Time** \\ \end{tabular} } & \multirow{3}{*}{\begin{tabular}{c} **Rework** \\ **Component** \\ **Amount** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Expected** \\ **Remwork** \\ **Time** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Re realized** \\ **Rework** \\ **Time** \\ \end{tabular} } \\ \hline P01 & 93 & 0 & 9 & P01 & 8 & & & & \\ \hline P02 & 87 & 30 & 8 & P02 & 9 & & & \\ \hline P03 & 64 & 40 & 6 & P03 & 5 & Yes & 8 & 3 & 4 \\ \hline P04 & 116 & 60 & 11 & P04 & 12 & & & \\ \hline P05 & 68 & 0 & 6 & P05 & 6 & & & \\ \hline P06 & 121 & 60 & 11 & P06 & 12 & & & \\ \hline P07 & 168 & 0 & 15 & P07 & 15 & & & \\ \hline P08 & 194 & 20 & 18 & P08 & 19 & & & \\ \hline P09 & 103 & 0 & 9 & P09 & 10 & Yes & 15 & 5 & 5 \\ \hline P10 & 54 & 30 & 5 & P10 & 5 & & & \\ \hline P11 & 102 & 60 & 9 & P11 & 9 & & & & \\ \hline P12 & 82 & 10 & 8 & P12 & 8 & Yes & 18 & 6 & 6 \\ \hline P13 & 157 & 30 & 14 & P13 & 12 & & & & \\ \hline P14 & 124 & 20 & 11 & P14 & 11 & & & & \\ \hline P15 & 120 & 30 & 11 & P15 & 12 & & & \\ \hline P16 & 109 & 60 & 10 & P16 & 11 & Yes & 18 & 6 & 7 \\ \hline P17 & 128 & 20 & 12 & P17 & 11 & & & & \\ \hline P18 & 165 & 90 & 15 & P18 & 17 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: (a) Parameters in the beginning; (b) realized parameters. As can be seen in Table 2 (parts a,b), the sometimes realized processing times differ the from expected processing times, and reworks also make important disturbance for the system as a completely new job. Initial scheduling is conducted before production starts.