# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 2 Related Studies  
In recent years, significant research studies have been undertaken to investigate the optimal railway maintenance scheduling. The approach by [PERSON] et al. [12] focused on allocating the maintenance tasks in the Jutland peninsula, the largest region in Denmark, to a set of maintenance crew members, where each crew undertakes a sub-region. The goal was to minimize the distance between two different tasks in the same sub-region by proposing a perturbative hyper-heuristic framework. [PERSON] et al. [13] presented a Decision Support System (DSS) applied in a real dataset in Southern Italy. The problem aimed to reschedule the timetable in real time and solve conflicts in the network for unexpected disturbances. The objective was to minimize the cost of delays. A different study was conducted by [PERSON] et al. [14] which intended to discuss current literature approaches for optimization in maintenance planning and scheduling, including possible gaps related to decision-making models. One of the observations was about the decision support models that are cost-based which often combine various costs to minimize the overall cost. Regarding the cost, they expect a stronger emphasis on environmental and other sustainability-related costs. In their study, [PERSON] et al. [15] proposed an automatic rescheduling algorithm for the real-time control of railway traffic and tested it in simulation on the Dutch railway network. The scope of this was to minimize the delays caused by disruptions. They used a Model Predictive Control (MPC) algorithm, while the rescheduling problem was solved by mixed integer linear programming using macroscopic and mesoscopic models. [PERSON] et al. [16] developed a model that focuses on disruptions tested in the Dutch railway traffic system, proposing an innovative bi-level rescheduling algorithm based on a mesoscopic mixed integer linear programming. The technique manages to obtain a feasible rescheduled timetable in a short computation time including safety constraints and capacity. An approach for the preventive signal maintenance crew scheduling problem in the Danish railway system was conducted by [PERSON] et al. [17], which was formulated as a mixed integer optimization model. The objective was to minimize the number of working days, to ensure that as many tasks as possible are completed inside the planning horizon and to minimize the penalty for assigning crew members. Another study by [PERSON] et al. [18] developed a model for planning preventive maintenance in the railway signaling system in Denmark. The problem was formulated as a multi-depot vehicle routing and scheduling problem with time windows and synchronisation constraints. Some tasks require the simultaneous presence of more than one engineer, which requires the consideration of task synchronization. Furthermore, a constraint programming (CP) approach was used to create viable monthly schedules for substantial, practically relevant scenarios, while the experimental results indicated that the proposed framework can generate feasible solutions and can schedule up to 1000 tasks for a monthly plan of eight crew members. Apart from the conventional optimization approaches for railway operations and maintenance, there exist solutions using Artificial Neural Networks (ANN). First, in the study of [PERSON] and [PERSON] [19], the Train Formation Problem (TFP) was formulated as a Back-Propagation Neural Network (BPNN) model consisting of three layers: the input layer representing O-D demands, a hidden layer, and the output layer representing the trains with the assigned demand. Their main objective was to utilize neural networks for obtaining near-optimal solutions in short periods of time, due to the high computational time of conventional solution algorithms producing train formation plans. Furthermore, [PERSON] et al. [20] were the first to implement maintenance planning for metro trains with an ANN model incorporating all train equipment and factors affecting the failure.