## 4 Solution Procedure
#### Sequencing the Processing of Orders  
In sequencing, the order in which cups of different volumes are processed is determined. The situation becomes complicated when a machine is heavily loaded, and many customer orders are involved. The order of processing is crucial as it affects the waiting \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Order No.** & \(\beta_{\text{yigk}}\) **(mL/sec)** & \(\gamma_{\text{yigk}}\) **(mL/sec)** & \(S_{\text{b}}\) **(cm/sec)** & \(E_{\text{g}}\) **(sec)** & \(P\) **(sec)** & \(F_{\text{a}}\) **(sec)** \\ \hline
1 & 50 & 3.76 & 5.38 & 552.4 & 27.9 & 580.3 \\
2 & 50 & 5.56 & 5.56 & 426.6 & 27.0 & 453.6 \\
3 & 50 & 5.56 & 2.78 & 259.2 & 54.0 & 313.2 \\
4 & 50 & 2.63 & 3.16 & 323.0 & 47.5 & 370.5 \\
5 & 50 & 2.63 & 1.75 & 324.9 & 85.5 & 410.4 \\
6 & 50 & 3.76 & 1.79 & 485.5 & 83.7 & 569.2 \\ \hline \end{tabular}
\end{table} 
Table 2: Optimal solution. time of the cups in queues and the idle time of the machine. One of the categories in priority sequencing rules is single-dimension rules, which determine priority based on a single aspect such as due date, processing time, or the arrival time at the machine. The data from the problem solved in Section 2 are considered for single-dimension priority rules, e.g., Earliest Due Date (EDD), Shortest Processing Time (SPT), and First Come First Serve (FCFS), as shown in Table 3.  
The EDD rule states that the third order is the one with the closest due date. Consequently, the third order is processed first and then the second one. The sixth order, with its due date furthest, is processed last. The sequence is shown in Table 4 along with flow time, minutes early, and minutes past due, with average values of 26.19, 0.30, and 10.99, respectively. Under the SPT rule, the sequence starts with the order that has the shortest processing time, which is the third one, and it finishes with the order that has the longest processing time, the fourth order. The sequence of orders is shown in Table 5. The average values of flow time, minutes early, and minutes past due for the SPT rule are 26.19, 1.73, and 12.42, respectively. With the FCFS rule, the sequence is started with an order in which the customer orders are received. Hence, the sequence starts with the first order and ends in the sixth order, which is received at last. The sequence is shown in Table 6 along with flow time, minutes early, and minutes past due, with average values 27.56, 0.06, and 14.54, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Order** & **Minutes Since** & **Starting** & **Processing** & **Finish** & **Flow** & **Scheduled** & **Actual Pickup** & **Minutes** & **Minutes** \\
**No.** & **Order Arrived** & **Time** & **Time** & **Time** & **Time** & **Pickup Time** & **Time** & **Early** & **Post Due** \\ \hline
3 & 1 & 0 & 5.22 & 5.22 & 6.22 & 7 & 7 & 1.78 & - \\
2 & 1 & 5.22 & 7.56 & 12.78 & 13.78 & 9 & 12.78 & - & 3.78 \\
1 & 0 & 12.78 & 9.67 & 22.45 & 22.45 & 10 & 22.45 & - & 12.45 \\
5 & 3 & 22.45 & 6.84 & 29.29 & 32.29 & 15 & 29.29 & - & 14.29 \\
4 & 0 & 29.29 & 6.16 & 35.45 & 35.45 & 20 & 35.45 & - & 15.45 \\
6 & 2 & 35.45 & 9.49 & 44.94 & 46.94 & 25 & 44.94 & - & 19.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Sequence of orders based on EDD rule. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Order No.** & **Minutes Since Order Arrived** & **Processing Time (Minutes)** & **Pickup Time (Minutes)** \\ \hline
1 & 0 & 9.67 & 10 \\ \hline
2 & 1 & 7.56 & 9 \\ \hline
3 & 1 & 5.22 & 7 \\ \hline
4 & 0 & 6.16 & 20 \\ \hline
5 & 3 & 6.84 & 15 \\ \hline
6 & 2 & 9.49 & 25 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The processing and pickup times of the set of orders. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Order** & **Minutes Since** & **Starting** & **Processing** & **Finish** & **Flow** & **Scheduled** & **Actual Pickup** & **Minutes** & **Minutes** \\
**No.