# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 2 Related Studies
### Optimization of Railway Line Maintenance Scheduling  
One area of research is concerned with the scheduling of maintenance operations to prevent disruptions to and from scheduled train routes, while also devising strategies to minimize infrastructure downtime and reduce maintenance costs. The study by [PERSON] [22] addressed the conflict between maintenance task scheduling and assigning them to crews within a given timetable. The goal was to achieve the optimal distribution of maintenance and crew activities to minimize disruptions to scheduled routes and reduce their duration. [PERSON]'s [22] approach was a heuristic tabu search for the order of tasks and maintenance crews. The model had specific constraints concerning the available budget, priority of maintenance activities, line availability, and minimum travel time between connecting lines. [PERSON] et al. [23] dealt with the optimization of resource allocation for task execution. They used the constraint language CHIP to solve real-world resource allocation problems. The problem aimed to map railroad lines to a given set of scheduled maintenance tasks, subject to certain constraints. As an example of the model's constraints, one involved the requirement to ensure that resources remained within the available limit. Another objective was to create a framework that maximizes task assignments based on their pre-defined priority. The approach by [PERSON] and [PERSON] [24] focused on preventive maintenance by exploring optimal track possession intervals for task execution. They mainly utilized train-free periods, resulting in a 33% reduction in track possession and associated costs, by combining works. Additionally, [PERSON] et al. [25] emphasized grouping small routine works and larger projects, scheduling them within specific periods to minimize maintenance costs without burdening train traffic. They employed mathematical programming formulations and heuristic solutions due to the complexity of the problem. In contrast to the previously mentioned studies, [PERSON] and [PERSON] [26] investigated the scheduling of a maintenance crew where various maintenance tasks were to be scheduled for a set of maintenance groups. One of the constraints was related to the direction a maintenance group followed during the execution of a task, i.e., from one task to the next. Furthermore, a constraint was defined that each task can be executed exactly once by a maintenance crew. [PERSON] et al. [27] adopted a completely different approach, where maintenance tasks incur penalties in the form of costs until the specific task is completed. The longer the task execution time, the higher the penalty cost was. The problem was formulated as a Vehicle Routing Problem (VRP), developing, and comparing it with different Mixed-Integer Linear Programming (MILP) models and customer costs concerning the time of execution. It should be noted that the vehicle routing problem of this study, unlike the common VRPs, minimized the sum of travel expenses and customer costs that depend on time. On the other hand, [PERSON] et al. [28] created a model in which each segment of the infrastructure was made available for maintenance at least once every four weeks. The main objective was to minimize maintenance costs. They defined a Single-Track Grid (STG), which is a traffic management system for railroad lines consisting of a single track. In this system, they divided the railroad line into work zones between stations, where each work zone defined a segment of the line for maintenance tasks which could be taken out of service for train traffic. They then utilized a Mixed-Integer Programming (MIP) model to define the single-track grids in shifts to create the maintenance schedule. Another study focusing on minimizing maintenance costs was conducted by [PERSON] et al. [29], who modelled short-term track maintenance scheduling within an existing timetable and maintenance program. The model included not only the tasks but also the assignment of tasks to maintenance crews.