# Dynamic Job and Conveyor-Based Transport Joint Scheduling in Flexible Manufacturing Systems
## 4 Exploring the Solution Space
### Detailed Solution
The case with the transport system shows a higher deviation since the instances have a lower number of jobs. Overall, the total rescheduling strategy provides near-optimal solutions with a limited use of the processing resources. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Id**} & \multicolumn{3}{c}{**Experim.-I**} & \multicolumn{3}{c}{**Experim.-II**} \\ \cline{2-7}  & **Sched-T** & **Actual** & **Err.** & **Sched-T** & **Actual** & **Err.** \\ \hline
1 & 1362 s & 1343 s & +1.41\% & 1107 s & 1412 s & \(-\)21.60\% \\
2 & 2444 s & 2436 s & +0.33\% & 2214 s & 2721 s & \(-\)18.63\% \\
3 & 3575 s & 3685 s & \(-\)2.99\% & 3231 s & 4239 s & \(-\)23.78\% \\
4 & 4796 s & 4775 s & +0.44\% & 4428 s & 5557 s & \(-\)20.32\% \\
5 & 6041 s & 5929 s & +1.89\% & 5354 s & 6945 s & \(-\)22.91\% \\
6 & 6973 s & 7189 s & \(-\)3.00\% & 6488 s & 8428 s & \(-\)23.02\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modified layout scheduling instances with transport. Figure 8: Difference (in percentage) between the makespan updated at every job arrival and the makespan from the ideal clairvoyant scheduler. Left and right figures refer to instances in [16] and the ICE instances. ## 6 Conclusions

Estimating the start and finish time of tasks belonging to jobs is fundamental for improving the efficiency of the manufacturing system. This is even more important in a fully automated environment, in which tasks are typically frequent but short. Integrating task duration with transport times enables more robust control of the overall process. To this aim, we designed a scheduler based on stochastic local search, which explores the solution space with a randomized approach. Our proposed heuristic, Sched-T, allows for building accurate and near-optimal schedules in a limited amount of time. This allows for efficiently managing the dynamic scenarios in which jobs continuously arrive or when unexpected events, such as machine breakdowns or maintenance activities, may occur. In the future, we plan to extend our heuristic to include stochastically variable task-processing times and evaluate their impact on overall efficiency. Conceptualization, S.G. and D.C.; investigation, S.G. and D.C.; methodology, D.C.; software, S.G. and D.C.; writing--original draft preparation, S.G. and D.C.; writing--review and editing, S.S.; supervision, S.S. and F.F. ; project administration, F.F. All authors have read and agreed to the published version of the manuscript. This work was partially funded by the Italian Ministry for University and Research (MUR) under the project _\"Joint Communication and Sensing: CSI-Based Sensing for Future Wireless Networks (CSI-Future)\"_, PRIN 2022-NRRP Mission 4, CUP D53D23016040001. The research was partially supported by the Italian National Group for Scientific Computation (GNCS-INDAM). Thisstudy was carried out within the PNRR research activities of the consortium iNEST (Interconnected North-Est Innovation Ecosystem) funded by the European Union Next-GenerationEU (Piano Nazionale di Rippresa e Resilienza (PNNRR) - Missione 4 Componente 2, Investimento 1.5-D.D. 1058 23/06/2022, ECS_0000043). This manuscript reflects only the Authors' views and opinions, neither the European Union nor the European Commission can be considered responsible for them. Not applicable. ## References

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