# Combined Optimization of Maintenance Works and Crews in Railway Networks
## 1 Introduction  
Transportation is a vital sector for society, as it profoundly influences daily citizen services and the economy. Notably, the railway sector has evolved into one of the safest and most environmentally friendly modes of transportation, encompassing primarily freight and passenger transport. The global railway network spans over an extensive 1.3 million kilometres worldwide, with the United States boasting the longest railway network, while Japan earned recognition for having the highest quality of railway infrastructure in 2019 [1]. Analyzing statistics from 2015 to 2021, it is evident that the demand for railway passenger transport experienced significant growth in the European Union until 2019. From 2019 to 2021 the statistics show a remarkable drop due to the pandemic of COVID-19 [2]. For instance, in 2016, Germany recorded the highest number of railway passenger trips, estimated at around 2.8 billion passengers [3]. Furthermore, Rail Freight Forward, representing a substantial 90% of Europe's rail freight transport, aims to elevate the share of railway freight transport from 18% to 30% by the year 2030. This ambitious goal has the potential to reduce approximately 25 million tons of CO\({}_{2}\) emissions [4]. Nonetheless, the prevailing requirements necessitate the railway industry to augment its capacity by introducing more trains with higher speeds and greater carrying capabilities. However, this progressioncomes with a drawback, as it leads to the deterioration of railway infrastructure and escalates maintenance costs. European countries allocate a significant sum, approximately EUR 15 to 25 billion annually, towards the maintenance and renovations of their railway systems [5]. These financial commitments underscore the importance of sustaining and enhancing the railway network to meet evolving demands while ensuring its long-term efficiency and environmental sustainability. The railway infrastructure should provide dependable conditions, thereby circumventing substantial disruptions in both passenger and freight transport operations. As such, the primary objective of railway line maintenance is to attain consistently high standards of safety and functionality while optimizing both time and cost factors. The economic significance of maintenance also becomes evident, as evidenced by the European railway network's expenditure, which surpassed EUR 25 billion in 2016, compared to EUR 20 billion in 2011. Notwithstanding this noteworthy cost escalation, budgets allocated for railway maintenance remain constrained, compelling infrastructure operators throughout the continent to explore strategies for accomplishing more with limited resources and achieving improved control over maintenance expenses [6]. Maintenance activities within the railway infrastructure can be broadly categorized into two main groups: inspection, which involves identifying and evaluating the current condition of the infrastructure, and restoration, focusing on rectifying already identified defects. Regular inspections are conducted at predetermined intervals, while emergency inspections occur to prevent potential incidents or address observed abnormalities during train operations. Special inspections are carried out at specific points with known risks, such as areas prone to landslides. The frequency of consecutive regular inspections adheres to predetermined time intervals. Restoration works can be further divided into three categories: material maintenance, which entails the replacement of sleepers, rails, and fastening elements; geometry maintenance works, involving track lifting and realignment; and ongoing maintenance tasks, such as leveling and aligning the track and lubricating switch points. [PERSON] et al. [7] focused on the preventive maintenance of railway tracks with ballast for compression works, and their model allows the analysis of maintenance actions over time, with longer analysis periods leading to better maintenance planning.