## 5 Results and Discussion  
The Laboratory of Computer Integrated Manufacturing, Industrial Engineering Department, King Saud University, Saudi Arabia, provided the basic information and data used in the computational results, and it corresponds to a real problem solved in the laboratory. The algorithm was solved using MATLAB programming language on a computer, and the results were obtained with a Core i7 and 1.99 GHz processor at a reasonable computational time. The aim was to maximize the speed of the conveyor belt, the feed rate of the yogurt, and flavor valves for the purpose of improving the throughput. The challenging issues were to find the optimal solution for the throughput maximization within a short time by finding the maximum feed rates of yogurt and flavor valves and the maximum speed of the conveyor belt less than or equal to the allowable limits. This was an interesting study as a team of researchers of the Department of Industrial Engineering were working on the yogurt filling machine directly, and it was a convenient sample for data collection and finding the results of the model developed. It was also easy for us to trace the results after implementation. In the previous sections, the optimal solution was found, and the results were considered for single-dimension priority rules. This section comprises two subsections. In the first, the effect of the change in the maximum value of feed rate of yogurt valve on the decision variable, \(S_{b}\), \(E_{n}\), \(P\), \(F_{n}\), and different performance measures were analyzed. While in the second subsection, the effect of change in the length of the conveyor belt on the decision variable, \(S_{b}\), \(E_{n}\), \(P\), \(F_{n}\), and different performance measures were investigated. The Effect of Change in Yogurt Flow Rate at Decision Variable, Parameter, Different Times and Performance Measures  
The effect of change in yogurt feed rate at the flavor feed rate, speed of conveyor belt, waiting time of the last cup of an order for processing, the processing time for a cup, total processing time on a cup, and performance measures (average flow time, average minutes early, average minutes past due) was analyzed in this subsection. The flow rate of the flavor valve changed from 51 mL/sec with an increment of 1 unit 55 mL/sec. During this change, the length between any two points (placement to yogurt filling, yogurt filling to flavor filling, and flavor filling to leaving) is considered 30 cm. The maximum speed of the conveyor belt is 10 cm/sec. As depicted in Figure 4, with an increase in the feed rate of yogurt, the flavor flow rate increases linearly. It can be observed that with the change in the yogurt feed rate, changes in the flavor flow rate of orders 1 and 6, 2 and 3, and 4 and 5 are equal. Moreover, due to \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Order** & **Minutes Since** & **Starting** & **Processing** & **Finish** & **Flow** & **Scheduled** & **Actual** & **Minutes** & **Minutes** \\
**No.** & **Order Arrived** & **Time** & **Time** & **Time** & **Time** & **Pickup Time** & **Pickup Time** & **Pickup Time** & **Early** & **Past Due** \\ \hline
1 & 0 & 0 & 9.67 & 9.67 & 9.67 & 10 & 10 & 0.33 & - \\ \hline
2 & 1 & 9.67 & 7.56 & 17.23 & 18.23 & 9 & 17.23 & - & 8.23 \\ \hline
3 & 1 & 17.23 & 5.22 & 22.45 & 23.45 & 7 & 22.45 & - & 15.45 \\ \hline
4 & 0 & 22.45 & 6.16 & 28.61 & 28.61 & 20 & 28.61 & - & 8.61 \\ \hline
5 & 3 & 28.61 & 6.84 & 35.45 & 38.45 & 15 & 35.45 & - & 20.45 \\ \hline
6 & 2 & 35.45 & 9.49 & 44.94 & 46.94 & 25 & 44.94 & - & 19.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Sequence of orders based on FCFS rule. the higher ratio of the flavor of yogurt in a required volume of a cup, the change in the feed rate of flavor in the case of orders 2 and 3 is greater than 1 and 6, and 4 and 5. As shown in Figure 5, an increase in the feed rate of the yogurt valve increases the speed of the conveyor belt linearly.