# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 2 Related Studies
### Optimization of Maintenance Scheduling to Minimize the Impact on Circulation
\begin{table}
\begin{tabular}{p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Authors (Year)** & **Objective** & **Mathematical Formulation** & **Solution Method** & **Application** \\ \hline [PERSON] and [PERSON] (2011) [31] & Minimize the total costs of planned maintenance and renewal actions and the total number of train delays caused by speed restrictions & Bi-objective integer nonlinear programming & Metaheuristics (Simulated annealing technique) & Metaheuristics (Simulated annealing technique) & Artificial network \\ \hline [PERSON] et al. (2019) [32] & Minimize the trade-off between condition deterioration and maintenance costs & Mixed-integer-linear programming & Scenario-based approach, Robust scenario-based approach & Case study (Randstad south and middle-south region, The Netherlands) \\ \hline [PERSON] et al. (2021) [33] & Minimize the workload for work crews and the hindrance of train operators by minimizing the maximum workload of all crews combined & Mixed-integer-linear programming & Exact solution (branch-and-bond) Metaheuristics (Simulated annealing) & Case study (The Netherlands) \\ \hline [PERSON] et al. (2022) [34] & Representing total costs and exploring the trade-off between this cost and the number of hard constraint violations & Constraint programming model & Evolution strategy, greedy metaheuristic, a hybrid of the two & Case study (The Netherlands) \\ \hline [PERSON] and [PERSON] (2017) [37] & A cost sum to be minimized for 5 cost components & Mixed-integer-linear programming & Exact solution (GUROBI) & Artificial network \\ \hline [PERSON] et al. (2019) [38] & Minimize the total deviation from the nominal timetable. Maximize the number of paired works & Mixed-integer-linear programming & Exact solution (IBM-ILOG-CPLEX) & Artificial network \\ \hline [PERSON] et al. (2013) [39] & Minimize the sum of train and maintenance delays & Problem Space Search (PSS) & Metaheuristics & Case study (Queensland, Australia) \\ \hline [PERSON] et al. (2013) [40] & Minimize the number of resource conflicts and cancelled trains & Mixed-integer- programming & Exact solution (CPLEX) & Case study (Sweden) \\ \hline [PERSON] et al. (2023) [35] & Minimize the cost caused by hindrance over train operators. Maximize the number of scheduled slots in the maintenance schedule. & Multi-objective model, Integer-linear programming & Metaheuristic and e-constraint method & Case study (The Netherlands) \\ \hline [PERSON] et al. (2019) [36] & Allocate time windows for railroad track maintenance to minimize the impact on train circulation & No formulation & Metaheuristic— Simulated Annealing for Track-block Optimization (SATO), Train Scheduling & Artificial network \\ \hline [PERSON] et al. (2005) [30] & Divide the Dutch railway infrastructure into working zones & No formulation & Optimal rules for the working zone division & Artificial network \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cont. This study focuses on examining the problem of scheduling a one-year preventive maintenance work plan. The goal is to identify the specific tasks and their corresponding time periods required to complete them, all aimed at minimizing the overall downtime of the infrastructure due to maintenance activities. In addition, we aim to provide a higher efficiency of operations, grouping them in the best possible way in terms of economic benefit and efficiency and balancing the workload for the maintenance crews. The maintenance works included in this study refer to two types, short-term/routine works (e.g., track and switching inspection, railway inspection, signaling systems, switch lubrication) and long-term/project works (e.g., ballast cleaning, rail grinding, compaction). Long-term works require more time to complete than routine works and are usually carried out once/twice in a few years. From the reviewed studies, the closest prior comparator to our work is the study of [PERSON] and [PERSON] [24] which we use as a baseline model.