## 5 Application  
The reference implementation of CoJoSim was applied to evaluate and compare different dispatching rules. For this purpose, 120 days were simulated and the manufacturing feedback data were continuously recorded to calculate key performance indicators (KPIs). These KPIs were then visualized and analyzed using throughput diagrams [56]. Since these diagrams focus on quantities without considering adherence to delivery dates, the output during the reference period in the throughput diagrams was split and colored for jobs that were early, late, and on time. To calculate adherence to delivery dates, early jobs and on-time jobs were summed. For more information on calculating KPIs and logistic targets, as well as analyzing throughput diagrams, the literature [7; 56] can be referred to.In the application, five dispatching rules were evaluated and combined. The first rule used was first-come-first-served (FCFS), which was used as a reference and is also the basic way of prioritization in the underlying MIMAC. The second rule is priority classes (PC), a rather simple dispatching rule. The third rule is delta flow factor (DFF), which considers the tardiness of the jobs. The fourth rule is shortest remaining processing time (SRPT), which prioritizes jobs with a higher degree of completion. The fifth rule is a slack-based dispatching rule (Slack), which combines DFF and SRPT. Figure 6 shows the throughput diagram for FCFS, which serves as a reference for comparing the other four dispatching rules. Table 4 presents the results of the four simulated dispatching rules for prioritizing jobs in CoJoSim. FCFS has a mean throughput of 6275 standard days (for a 120 working days simulation duration) and a mean adherence to delivery dates of 71.36% and is used as a reference. The following dispatching rules have the common objective of influencing and improving adherence to delivery dates compared to this reference. With DFF and SRPT, mean throughput and mean adherence to delivery dates can be slightly increased compared to the reference. A significant improvement is possible with PC, and the best results are achieved with Slack. An improvement in adherence to delivery dates of almost 15 percentage points was achieved by Slack compared to the reference. The throughput diagram for Slack is shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Dispatching Rule** & \multicolumn{2}{c}{**Standard Days**} & \multicolumn{2}{c}{**Adherence to Delivery Dates**} & \multicolumn{2}{c}{**Jobs Early**} & \multicolumn{2}{c}{**Jobs on Time**} & \multicolumn{1}{c}{**Jobs Late**} \\ \hline First-Come-First-Served & FCFS & 6275 & 71.36\% & 55.65\% & 15.71\% & 28.64\% \\ Delta Flow Factor & DFF & 6379 & 74.62\% & 54.65\% & 19.97\% & 25.38\% \\ Shortest Remaining & SRPT & 6523 & 75.12\% & 59.02\% & 16.10\% & 24.88\% \\ Proparity Classes & PC & 6681 & 81.82\% & 62.28\% & 21.54\% & 16.18\% \\ Combination of & Slack & 6714 & 85.83\% & 54.96\% & 30.87\% & 14.17\% \\ DFF \& SRPT & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Structure of manufacturing feedback data. When reviewing the results, it is remarkable that PC, a rather simple dispatching rule, performs comparatively well. This is likely due to matching prioritization at bottlenecks. However, it is also clear that this dispatching rule is too simplistic for real-world applications. DFF and SRPT both improve performance compared to the reference only slightly. However, combining both with Slack achieves the best results in the analyzed application. This observation can presumably be explained by the fact that meeting delivery dates plays a significantly smaller role at the beginning of the work route than at the end and that jobs with a higher degree of completion tend to be prioritized by Slack. Therefore, a hierarchy of different dispatching rules is usually used in practice as well [57]. Other important parameters in production control, such as machine utilization rate or  
Figure 6: Throughput diagram for first-come-first-served.