# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 5 Results  
The implementation of the model was conducted on a conventional computing machine with an AMD Ryzen 7 5800H processor and 16 GB RAM and was solved in 24 s. The results are reported mainly in the form of produced timetables for the maintenance works and the work crews. Using the methodology described above, they refer to the scheduling of maintenance operations and the work crews. First, Figure 1 represents the scheduling of projects and routine works to be allocated to each link optimally within one year. The colored points depict the tasks required for each category at any given time. As can be seen, the model's results adhere to the different constraints imposed, including starting times, frequencies, and durations. Based on the model presented, the tasks needed to be assigned to the respective crews. They have been divided into five different work crews; in addition to the main links, there is also the link {L0}, which represents the depot. As mentioned before, if the work crews are not performing scheduled tasks they end up in the depot, and thus we know the total movement of each crew at any given time. The depot is common to all crews and is a reference point (the point where all workers must assemble and collect their maintenance equipment before performing any maintenance activity). As an example, Figure 2 depicts the fourteen maintenance tasks which were allocated to crew number one. The fundamental requirements ensure that every week, each crew must be assigned to scheduled tasks or remain stationed at the depot. Additionally, a particular task cannot be handled by two different crews. The workload of the crews is distributed in a manner that maintains relative equality among them. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Links** & **L1** & **L2** & **L3** & **L4** & **L5** \\ \hline \multirow{8}{*}{Combinations of tasks} & (P1, R4) & (P1, R4) & (P1, R4) & (P1, R4) & (P1, R4) \\ \cline{2-6}  & (P1, R3) & (P1, R3) & (P1, R3) & (P1, R3) & (P1, R3) \\ \cline{2-6}  & (P1, R5) & (P1, R5) & (P1, R5) & (P1, R5) & (P1, R5) \\ \cline{2-6}  & (P1, P2) & (P1, P2) & (P1, P2) & (P1, P2) & (P1, P2) \\ \cline{2-6}  & (P2, R4) & (P2, R4) & (P2, R4) & (P2, R4) & (P2, R4) \\ \cline{2-6}  & (P2, R3) & (P2, R3) & (P2, R3) & (P2, R3) & (P2, R3) \\ \cline{2-6}  & (P2, R5) & (P2, R5) & (P2, R5) & (P2, R5) & (P2, R5) \\ \cline{2-6}  & (R3, R4) & (R3, R4) & (R3, R4) & (R3, R4) & (R3, R4) \\ \cline{2-6}  & (R3, R5) & (R3, R5) & (R3, R5) & (R3, R5) & (R3, R5) \\ \cline{2-6}  & (R4, R5) & (R4, R5) & (R4, R5) & (R4, R5) & (R4, R5) \\ \cline{2-6}  & (R3, P1) & (R5, P2) & & (R4, P2) & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Combinations of routine works and projects. The first crew returns to the depot after performing a single task from the beginning until week seven. Furthermore, the crew stays at the depot for twelve weeks, between weeks thirty-two and forty-three. Similarly, work crew number two performs sixteen tasks. It is noticed that the tasks begin in the first and second week, followed by seven weeks at the depot before the next task is assigned. Following the completion of the task, there is a six-week period of stay at the depot. Unlike the concentrated weeks spent at the depot, the period of intense work spans from the twenty-eighth to the forty-third week, with only a few weeks spent at the depot during this time. Crew number three performs thirteen maintenance tasks. Initially, it carries out two consecutive tasks and then remains  
Figure 1: Scheduled maintenance tasks (in color). Figure 2: Maintenance tasks allocated to Crew Number 1 (in green color). at the depot for eighteen weeks. Most of the work is executed without prolonged stays at the depot, taking place between week twenty-one and week thirty-nine. During this period, seven maintenance tasks are performed at regular intervals of one week, two weeks, or none. For crew number four, it has been observed that maintenance tasks are evenly distributed throughout the fifty-two weeks.