# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 5 Results
The weeks, compared to the above-mentioned crews, remaining in the depot are fewer in aggregate over several weeks. The longest period in the depot is eight consecutive weeks and occurs in weeks twenty-nine to thirty-seven. The fifth crew is found to have the largest number of allocated tasks, equal to twenty-three. However, it is observed that sixteen of these tasks relate to the routine R4 and they are distributed approximately equally across all links. As a result, there can be optimal efficiency in completing the task R4, since this crew repeats the same task at regular intervals and thus knows the task requirements and communicates and collaborates better. Finally, the crew stays in the depot for twenty-nine weeks in total. In addition, an essential result of the model is depicted in Figure 3, as it illustrates both the total scheduling of maintenance works and their allocation to different work crews. Thus, there is supervision of the work crews that will perform the tasks. There are a total of 82 scheduled tasks on the various links, out of which three are assigned to the project P1, two to the project P2, and the remaining are routine works, with 14 for R3, 47 for R4, and 16 for R5. The seemingly high number of Routine R4 tasks is contingent on the frequency of tasks previously specified and validated based on the actual number of times they have been requested for execution. Similarly, the projects according to their possible starting time and duration in Table 3 are optimally allocated and verified. Project P1 has been executed with \(k\)= 1 in the twelfth to fourteenth week, P2 with \(k\) = 1 in the second week, and in the fifth week with \(k\) = 3. Furthermore, the pairs of combined tasks resulting in different links in the same week are: {[R3, R4], [P2, R3, R4], [R4, R5], [P2, R4], [P1, R4], [R3, R4, R5]}. According to the parameters we have defined, no task is performed on the same link simultaneously; rather, it is scheduled on different links, which helps to mitigate the track possession cost overhead. Additionally, the distribution of crews appears to be carefully planned, ensuring a balanced workload across all teams, and avoiding any undue burden on a particular crew. Finally, the scheduling of crew movements is optimized to minimize costs effectively. Figure 3: Scheduled maintenance tasks (in color) and crew allocations. In the following figures (Figures 4 and 5), a comparison between the results of the baseline model [24] and our proposed model is illustrated. In the study of [PERSON] and [PERSON] [24], only the first twenty weeks of planned maintenance tasks are given; thus, for comparison reasons, we have adjusted our results table based on the results from the baseline model. The numbering of routine works here is different, with {R1,R2,R3} routine works of the baseline model corresponding to {R3,R4,R5} in our model. From the above figures, one can observe that most of the scheduled activities are planned for the link L1 in both approaches. Overall, in comparison to the base model of [PERSON] and [PERSON] [24], the objective function has been extended. This is the case since different values have been included for certain parameters, (e.g., duration of projects, pairs of combined tasks, scheduling period of routine tasks). To conduct a comparative analysis with the base model, our model was solved while excluding the work crews' impact on the allocation of maintenance  
Figure 4: Annual maintenance planning—baseline model. _[PERSON] and [PERSON]_[24]. Figure 5: Annual maintenance planning—proposed model. tasks. The objective was to maintain identical conditions to the base model, with only the modifications specific to our approach considered. The maintenance work's total cost is EUR 8333, comprising EUR 8200 for track possession during each operation and EUR 133 for route cancellations and resource underutilization. In the base model, these costs were EUR 5700 and EUR 165, respectively.