# Efficient Task Scheduling Using Constraints Programming for Enhanced Planning and Reliability
## 5 Conclusions  
This study demonstrates the effectiveness of a constraint programming algorithm for efficient MRO workspace scheduling of aircraft engines. By leveraging data from Korean Air's MRO maintenance logs, the proposed method achieves a good scheduling efficiency  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Tasks**} & \multirow{2}{*}{**Work** **Places**} & \multirow{2}{*}{**Horizon**} & \multicolumn{3}{c}{**CP (Ours)**} & \multicolumn{3}{c}{**GA**} \\ \cline{3-8}  & & & **Days** & **Utilization** & **CPU [s]** & **Days** & **Utilization** & **CPU [s]** \\ \hline
3 & 3 & 175 & 61 & 95.63\% & 1.37 & 90 & 64.81\% & 11.63 \\ \hline
6 & 3 & 350 & 117 & 99.72\% & 2.82 & 181 & 64.46\% & 21.03 \\ \hline
9 & 3 & 525 & 175 & 100.00\% & 6.90 & 236 & 74.15\% & 30.27 \\ \hline
12 & 3 & 700 & 234 & 99.72\% & 22.77 & 292 & 79.91\% & 39.62 \\ \hline
24 & 3 & 1400 & 467 & 99.93\% & 26.93 & 548 & 85.16\% & 76.47 \\ \hline
24 & 4 & 1400 & 350 & 100.00\% & 56.32 & 456 & 76.75\% & 76.12 \\ \hline
24 & 5 & 1400 & 280 & 100.00\% & 132.96 & 365 & 76.71\% & 75.83 \\ \hline
24 & 6 & 1400 & 234 & 99.72\% & 73.49 & 331 & 70.49\% & 75.73 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Experimental results for various tasks and workplaces without minimum start days.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Tasks** & **Work Places** & **Days** & **CPU [s]** \\ \hline
3 & 3 & 76 & 1.30 \\ \hline
6 & 3 & 132 & 11.74 \\ \hline
9 & 3 & 190 & 35.07 \\ \hline
12 & 3 & 249 & 57.49 \\ \hline
24 & 3 & 470 & 26.93 \\ \hline
24 & 4 & 355 & 59.30 \\ \hline
24 & 5 & 289 & 145.93 \\ \hline
24 & 6 & 244 & 52.82 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Experimental results for various tasks and workplaces with minimum start days given.  
and resource utilization of up to 100%, with an average of 99.34%, highlighting its potential for broader application in the aviation industry.  
The CPU time analysis demonstrates that the constraint programming algorithm proposed in this study is highly efficient for solving small-to-medium-sized MRO scheduling problems. While CPU time increases as the number of tasks and workplaces grows, it remains within practical limits for the scenarios tested. Future research should focus on enhancing scalability through parallel computing, incremental scheduling, or hybrid approaches to handle larger and more complex MRO environments efficiently.  
By achieving a near-optimal utilization of resources and maintaining computational efficiency, this method holds significant potential for improving MRO operations in the aviation industry. However, to fully realize its potential, future research must address the current limitations and explore ways to scale the solution for larger, more dynamic environments. With further validation and refinement, this approach could play a crucial role in advancing the efficiency, reliability, and sustainability of aircraft maintenance practices.  
Methodology, S.J., D.K. and W.K.; Software, D.K. and W.K.; Validation, D.K. and W.K.; Formal analysis, W.K.; Investigation, J.C.; Resources, J.C. and K.Y.; Data curation, S.J.; Writing--original draft, W.K.; Writing--review & editing, S.J. and D.K.; Visualization, W.K.; Supervision, J.C. and K.Y.; Project administration, J.C.; Funding acquisition, J.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the Ministry of Land, Infrastructure and Transport's technology development program [RS-2023-00239124] and the Ministry of SMEs and Startups project \"Development of Open Smart Manufacturing Sharing Platform for Enterprise Linkage in Discrete Process Characteristic Industries\" [RS-2022-00140586].