# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 3 Methodological Framework and Problem Formulation  
In countries with a high frequency of train services, such as the Netherlands, maintenance activities are usually scheduled during the night to avoid major disruptions. Furthermore, certain long-duration works require the closure of the railway line and are scheduled during the night or at the weekends, or during low traffic volumes. In railway lines with a lower frequency, certain maintenance activities can be carried out during the day in free time gaps between two consecutive train passages. During a link closure for maintenance works, a rerouting must be planned, a detour from the main track route must be made, or the route must be cancelled. This depends primarily on the railway network topology of the location where the maintenance work is being conducted, and it constitutes one of the main reasons for timetable delays. Starting from the baseline model of [PERSON] and [PERSON] [24] which schedules the maintenance works, we focused on the integration and assignment of work crews to perform the scheduled tasks. This means that for every planned task at every time and each link, there must be a work crew available. In this configuration framework, a reference point was created for the start and end of the work crews, namely the depot. In this way, depending on the movement of the crews, their costs and their exact location can be calculated. Each crew must perform one of the three options that have been set. The three options refer to a crew staying at the same link, moving to a different link, or returning to the depot. The incorporation of the work crews into the baseline model holds significant importance, as it facilitates enhanced management of the annual preventive maintenance program. This is achieved by ensuring the availability of the necessary work crews and their associated costs from the outset. Additionally, it enables a comprehensive overview of planned maintenance works and provides time for implementing the necessary actions towards its execution. To develop the enhanced model, it was necessary to add to the base \begin{table}
\begin{tabular}{p{56.9 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Authors (Year)** & **Objective** & \begin{tabular}{c} **Mathematical** \\ **Formulation** \\ \end{tabular} & **Solution Method** & **Application** \\ \hline [PERSON] et al. (2018) [10] & \begin{tabular}{c} Minimize total cost in the whole planning horizon \\ \end{tabular} & \begin{tabular}{c} Integer-linear \\ programming \\ \end{tabular} & Exact solution (CPLEX) & Artificial Network \\ \hline [PERSON] et al. (2016) [11] & \
\begin{tabular}{c} Minimize the number of \\ cancelled trains and \\ minimize the decrease in \\ service level to the \\ passenger \\ \end{tabular} & Linear programming & Robust approach &
\begin{tabular}{c} Case study (Brussels, Belgium) \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._model new sets, parameters, decision variables, and constraints to meet our requirements. A configuration of the objective function was also carried out by including a new term. The base model of [PERSON] and [PERSON] [24] defined some tasks and links of the railway line. The tasks were divided into two categories, projects, and routine works. The projects involved maintenance works that took a long time to complete, and the link had to be taken out of service or carried out at the maximum train-free period length. On the other hand, routine works involved maintenance works with a shorter completion time and could be carried out in time gaps between the passage of two consecutive trains. The planning period was one year, i.e., T = 52 weeks. Moreover, a set of combined tasks for both projects and routine works was created, which could be performed simultaneously on the same link. In addition, it should be mentioned that there is a set of three options indicating the execution time of the projects.