## 6 Numerical Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Optimal Buffer Size** & **5** & & **5** & **5** & **5** & **5** \\ \hline  & **MTS** & **MTO** & **Dynamic P100** & **Dynamic P50** & **Dynamic P25** & \begin{tabular}{c} **Dynamic** \\ **Continuous** \\ \end{tabular}  \\ \hline Throughput & 2289.06 & \(-0.54\%\) & \(-3.97\%\) & \(-0.19\%\) & \(-0.15\%\) & \(-0.17\%\) \\ \hline Tardiness & 1,406,251.29 & \(17.64\%\) & \(9.15\%\) & \(7.94\%\) & \(7.02\%\) & \(7.26\%\) \\ \hline Earliness & 7315.82 & \(-88.51\%\) & \(-49.77\%\) & \(-47.42\%\) & \(-42.17\%\) & \(-44.15\%\) \\ \hline Average Time in System & 711.75 & 16.92\% & 6.46\% & 5.33\% & 4.48\% & \(4.70\%\) \\  
Figure 5 presents the average waiting time for customers (wait) for exponential parameters 12, 13, and 14, displayed as a percentage difference relative to the MTS baseline. For this performance measure, the increase in waiting time is notably limited when the exponential parameter is set to 12. This suggests that, similar to other performance metrics, the impact of the proposed policies on average waiting time is less pronounced in the case where the exponential parameter is 12, resulting in more favorable outcomes compared to the MTS. Figure 6 illustrates the work in process (WIP) for exponential parameters 12, 13, and 14, shown as a percentage difference relative to the MTS baseline. The proposed policies significantly reduce WIP compared to the MTS production system. Notably, for the exponential parameter set to 12, the dynamic policy with a periodic review interval of 25 achieves a reduction in WIP exceeding 30%, while its performance remains relatively close to that of the MTS. This substantial decrease in WIP highlights the effectiveness of the proposed policies in optimizing production efficiency. Figure 4: Deviation of average time in system. Figure 3: Average time in system. Based on the analysis of the numerical results, the following conclusions can be drawn:  
Effectiveness of Proposed Dynamic Policies: The proposed dynamic policies show better alignment with MTS performance when the exponential parameter is set to 12 for inter-arrival times. This indicates that the dynamic policies are more effective when the rate of customer orders is higher. Conversely, when the inter-arrival time is longer, the performance of the proposed dynamic policies deteriorates. Optimal Dynamic Policy: Among the dynamic policies tested, the periodic review with a review interval of 25 periods proves to be the most effective. The continuous review approach yields results that are comparable to those of the periodic review with a 25-period interval. This means that the periodic approach needs a lower interval to work better. Reduction in Work in Process (WIP): The most significant improvement offered by the proposed dynamic policies is the reduction in WIP. The reduction is 20% for an inter-arrival time of 14, approximately 35% for an inter-arrival time of 12, and 50% for  
Figure 5: Average customer waiting time. Figure 6: Work in process. an inter-arrival time of 13. The greatest reduction in WIP occurs when the inter-arrival time is intermediate, suggesting that the proposed policies are most effective in this range. Buffer Capacity and Performance: From the perspective of buffer capacity, the proposed dynamic policies perform better with the same capacity as the MTS, except when dealing with higher inter-arrival parameters. The most favorable trade-off between performance measures is achieved with an inter-arrival parameter of 12. In this scenario, while the performance is slightly worse compared to the MTS--by about 10%--there is a notable reduction in WIP of 35%. Overall, the proposed dynamic policies demonstrate considerable improvements, particularly in reducing WIP, though their effectiveness varies with the inter-arrival time. The periodic review with a 25-period interval emerges as the most advantageous approach, offering a good balance between performance and efficiency.