## 4 Case Study--Numerical Experiments
### Managerial Insights  
The analysis of buffer allocation in a steel manufacturing company's inter-facility material transfer operation and outbound logistics process reveals several key managerial insights. Firstly, the number and allocation of trucks significantly impact buffer optimisation and material transfer efficiency. By increasing the number of trucks allocated to each material type and the total number of trucks, the overall throughput in total tons of materials transferred can be increased. However, a potential decrease in the average throughput per truck may accompany this increase. Therefore, managers must carefully balance the number of trucks allocated to different material types to achieve optimal performance. Different optimal buffer allocations were obtained when different truck allocations were implemented for each material type while maintaining a constant total number of trucks, leading to varying throughput values. This finding highlights the importance of considering the quantity and composition of trucks when determining buffer requirements. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Scenario \#**} & \multicolumn{3}{c}{**Cycle Time (min)**} \\ \cline{2-4}  & **GEM Method** & **Simulation Model** & **Diff.** \\ \hline Scenario 1 & 13.471 & 14.69 & \(-\)8.30\% \\ \hline Scenario 2 & 13.851 & 14.69 & \(-\)5.71\% \\ \hline Scenario 3 & 12.981 & 14.12 & \(-\)8.07\% \\ \hline Scenario 4 & 12.135 & 12.63 & \(-\)3.92\% \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Comparison of cycle times using analytical and simulation methods. \begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Scenario \#**} & \multirow{2}{*}{
\begin{tabular}{c} **Optimal Buffer** \\ **Allocation** \\ \end{tabular} } & \multicolumn{2}{c}{**Throughput (\#**} & **Aver. Order** & **Total Number** \\  & & **of Orders** & **Processing** & **of Buffer** \\  & & **Processed)** & **Time (min)** & **Spaces Used** \\ \hline Scenario 1 & 1,1,5,1,7,1,4,3 & 49 & 14.69 & 23 \\ \hline Scenario 2 & 2,2,2,3,3,1,1,2 & 49 & 14.69 & 16 \\ \hline Scenario 3 & 1,1,1,1,1,1,1,1 & 51 & 14.12 & 8 \\ \hline Scenario 4 & 5,12,3,3,20,7,2,16 & 57 & 12.63 & 68 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimal buffer allocations for identified scenarios with order processing efficiency. Furthermore, the analysis reveals that an increase in the total number of trucks does not necessarily result in a proportional increase in buffer requirements. Different scenarios with equivalent numbers of trucks may require significantly different buffer allocations, depending on the truck composition and the specific service stations involved. Thus, managers should consider the specific characteristics of each scenario and carefully analyse the interplay between truck allocations, customer order compositions, and buffer requirements to optimise material transfer operations. The analysis also emphasises the significance of resource utilisation rates in identifying potential bottlenecks and improving system performance. By evaluating the utilisation rates of servers at various nodes or service stations, managers can pinpoint areas with high levels of occupancy that may hinder system efficiency. In particular, the analysis identifies nodes where utilisation rates approach or reach 1.0, indicating potential bottlenecks. These bottlenecks signal the need for reallocation or additional resources to ensure optimal system performance. Strategies such as process subdivision, workload consolidation, or adding servers can help balance the workload and enhance resource utilisation, reducing congestion and improving overall system efficiency. Sensitivity analysis further enhances decision making by assessing the impact of critical factors on system outcomes. The analysis demonstrates the influence on throughput, buffer allocations, and utilisation rates by introducing an additional server in specific scenarios.