Model for Planning and Optimization of Train Crew Rosters for Sustainable Railway Transport

Abstract

Efficient planning of train crew rosters is a key factor in ensuring operational reliability and promoting long-term sustainability in railway transport, both economically and socially. This article presents a systematic approach to developing a crew rostering model in passenger rail transport, with a focus on the operational setting of the train crew depot in Česká Třebová, a city in the Czech Republic. The seven-step methodology includes identifying available train shifts, defining scheduling constraints, creating roster variants, and calculating personnel and time requirements for each option. The proposed roster reduced staffing needs by two employees, increased the average shift duration to 9 h and 42 min, and decreased non-productive time by 384 h annually. These improvements enhance sustainability by optimizing human resource use, lowering unnecessary energy consumption, and improving employees’ work–life balance. The model also provides a quantitative assessment of operational feasibility and economic efficiency. Compared to existing rosters, the proposed model offers clear advantages and remains applicable even in settings with limited technological support. The findings show that a well-designed rostering system can contribute not only to cost savings and personnel stabilization, but also to broader objectives in sustainable public transport, supporting resilient and resource-efficient rail operations.

1. Introduction

The efficient organization of work shifts for train crews is a key factor in ensuring the smooth, safe, and high-quality operation of passenger rail transport [1,2]. Train crews—typically composed of conductors and train attendants—play an indispensable role in delivering passenger services, maintaining transport safety, and ensuring effective communication between the railway operator and the travelling public [3,4]. Given the complexity of operations, the high frequency of train services, and the regional variability of the railway network, the planning of crew rosters must be based on a rational system that balances technical–organizational [5,6], legal, and social requirements [7,8].

In addition to operational efficiency, the crew rostering process has significant implications for the broader goals of sustainable transport. Well-optimized shift schedules contribute to sustainability by improving resource utilization, reducing idle times and unnecessary train movements, minimizing employee fatigue, and fostering a healthier work–life balance, all of which align with the social and environmental dimensions of sustainable development. Moreover, efficient crew planning can reduce the overall energy consumption of rail operations by enabling more predictable and stable service patterns, which are critical for long-term sustainability in public transport systems [9,10].

In the context of European railway operators, the creation of crew rosters is governed by a wide range of legal and company-specific regulations [11,12]. These regulations set limits on maximum shift durations, rest periods, and the use of night or split shifts. In the Czech Republic, the legal framework includes the Labour Code [13], Government Decree No. 589/2006 Coll. [14], and company-level documents such as Regulation ČD K13 [15] and current collective agreements.

Sustainable rostering must also account for the specific technical and operational aspects of railway services, including turnaround times, deadhead movements, rest conditions during layovers outside home depots, and non-driving shifts [16,17,18,19]. As railways play an essential role in decarbonizing transport systems, optimizing crew schedules is not only a matter of logistics but also a strategic element in advancing sustainable mobility goals.

The aim of this article is to propose a crew rostering model that meets the conditions for practical implementation in a real operational environment, while also complying with legal working time limits. The study is applied to a case location the Train Crew Centre in Česká Třebová, which serves as a key passenger transport hub on the Czech Railways network.

An analysis of the existing rosters reveals several weaknesses, such as excessively long shifts, frequent split shifts, insufficient synchronization with rolling stock circulations, and excessive workload placed on certain employees. The proposed model therefore emphasizes the optimization of shift durations, balanced distribution of workload, minimization of non-productive activities, and consideration of employee preferences. The article applies a combination of analytical-descriptive methods, the use of planning systems such as the Comprehensive Automated Circulation System (in short KASO), and an empirical comparison of the current and proposed roster models in terms of operational feasibility and cost efficiency.

The ambition of this study is to contribute to the ongoing discourse on modern trends in human resource planning in railway operations, highlighting the need to align legal standards, carrier operational requirements, and employee well-being.

The innovative aspect of the presented research lies in the adaptation of existing methodologies to the environment of a regional crew depot (Train Crew Centre Česká Třebová), where standard planning software tools such as KASO are not available, and the option to exchange shifts between depots is lacking. In this context, a custom graphical method for roster optimization is proposed, which complies with applicable legislation while also considering employee preferences, minimizing disruptive factors (overnight rest periods away from the Home Depot), and ensuring operational efficiency. The research thus bridges the gap between theoretical models and their practical applicability in the specific conditions of regional railway operations.

The article is structured into several thematic sections that systematically reflect the individual phases of addressing crew scheduling in railway transport. The Introduction defines the main research objectives, highlighting its innovative character and practical contribution to optimizing human resources in the railway sector. The Literature Review summarizes current findings, scientific approaches, and algorithmic solutions applied in the planning and optimization of train crew rosters. Particular attention is given to studies from German, Dutch, Chinese, and American railway systems, comparing methodological frameworks and real-world implementations. The Methodology Section describes the procedural approach used in developing the new roster proposal, including the logic and rules applied in the construction of shift cycles and the planning of work shifts. Additionally, the effectiveness of the proposed roster is assessed. The Research Background outlines the preparatory technological processes, provides an overview of the current state at the Česká Třebová Train Crew Centre, and analyzes existing rosters. This section forms the analytical foundation for the proposed optimized solutions. The Results present the new roster design, emphasizing more efficient use of personnel capacity and detailing the calculated annual costs of implementation. Finally, the Discussion and Conclusion Sections compare the new findings with current practice, evaluating their benefits in terms of operational efficiency, cost-effectiveness, and potential applicability to other train crew centres.

2. Literature Review

Crew scheduling for passenger rail services constitutes a fundamental component of operational reliability and cost-efficiency in the railway sector. This issue is characterized by a high degree of complexity, as it must simultaneously consider technological, legislative, operational, and human resource constraints. Over the past decades, research in this field has increasingly focused on the application of operations research, advanced optimization algorithms [20,21], and integrated scheduling systems [22,23,24,25,26,27], while emphasizing the need to align efficiency with the social and organizational aspects of railway staff deployment [28,29,30]. This literature review provides a systematic overview of the current state of knowledge in the field of railway crew scheduling and optimization [31,32,33], thematically structured by applied methodological approaches, regional implementations, and recent trends in addressing this complex task. The selected literature has been reviewed with an emphasis on applicability in public passenger transport and on the practical experience of national railway operators.

2.1. Mathematical Modelling and Algorithmic Approaches

Among the dominant methods used in crew scheduling are integer programming (IP), linear programming, set partitioning, and column generation techniques. Several seminal studies [34,35,36,37] introduced fundamental models based on multi-commodity network flow formulations and demonstrated their implementation in solving crew planning problems in passenger transport. A classical approach also includes the use of set-partitioning models in the study [38], which enable efficient allocation of shifts among crew members. Efficient applications of column generation for real-world problems are presented in the studies [39,40], who focus on robust crew planning with respect to attendance variability. The authors of the study [41] improved the computational performance of column generation methods tailored to Japanese railway crew scheduling. Heuristic approaches also play a significant role, including three-phase heuristics designed for fairness in crew assignments in the study [42], tabu search algorithms in the study [43], and hybrid techniques involving discrete-event simulation in the study [44]. In the field of machine learning, emerging research includes hybrid models [45] that integrate deterministic and heuristic components to enhance the adaptability and performance of crew scheduling systems.

2.2. Regional Case Studies

The practical implementation of crew scheduling methodologies often varies depending on the operational context. In Germany, the issue has been addressed in the studies [46,47,48], who optimized crew rosters for regional passenger services operated by DB Regio and DB Schenker. These studies focus on aligning crew shifts with service demands while considering operational restrictions and regional work regulations. Dutch research [49,50,51] presents the implementation of advanced crew scheduling models within Netherlands Railways. These approaches incorporate iterative task allocation processes and multi-commodity flow methods, tailored to the specific characteristics of the Dutch rail system. In Asia, particular attention has been paid to high-speed railway crew scheduling in the studies [2,52,53]. These studies address complex planning challenges such as multi-depot operations and multi-license requirements, reflecting the organizational and technical complexities of Asian high-speed rail systems. In North America, large-scale optimization systems dominate. Research [54] focuses on solving large-scale multi-commodity crew scheduling problems in the context of expansive freight and passenger railway networks in the United States and Canada, often utilizing integrated planning platforms and advanced mathematical modelling.

2.3. Retiming, Fairness, and Equitable Crew Scheduling

Another important dimension of crew scheduling is the consideration of social and human factors. Fairness-based scheduling approaches [55,56] aim to ensure an equitable distribution of shifts among employees over extended time horizons. These models seek to balance workload, night shifts, and rest periods in a way that promotes well-being and long-term staff satisfaction. The article [57] introduced the concept of retiming, which involves time-shifting of shifts as a means of rescheduling crews in response to operational disruptions or adjustments in service patterns. Retiming strategies enhance the flexibility and resilience of crew schedules, particularly in dynamic operational environments.

2.4. Integrated and Real-Time Crew Scheduling

Integrated models aim to simultaneously address the scheduling of train services, vehicle circulations, and crew shifts. The authors of the article [58] introduced one of the first comprehensive approaches to this problem, establishing a foundation for coordinated planning across operational layers. These models typically leverage shared constraints and dependencies between timetables, vehicle rosters, and crew shifts to optimize overall system performance. The study [59] provides an extensive review of real-time algorithms designed to support rescheduling in response to disruptions, delays, or operational adjustments. These approaches are critical in modern railway systems where flexibility and responsiveness are essential. The authors of the study [60] presented a practical implementation of a decision support system tailored for strategic crew scheduling in passenger rail transport. Their model illustrates how real-time data and optimization tools can be integrated to support long-term planning decisions while maintaining operational feasibility in changing environments.

2.5. Trends and Challenges in Crew Scheduling

Recent studies [61,62] have emphasized the growing need to incorporate factors such as crew availability, legal regulations, and shift structures into the practical implementation of scheduling models. These elements are crucial for ensuring compliance and operational feasibility in real-world settings. One of the key challenges remains the integration of labour law constraints, attendance rates, night shift management, rest period allocation, and the balance between cost-efficiency and employee well-being [6,63]. These aspects demand sophisticated modelling approaches that can simultaneously address operational optimization and social fairness, particularly in contexts with limited planning resources or highly variable service patterns.

The presented literature review confirms that the problem of planning and optimizing railway crew rosters is a subject of intensive research at both national and international levels. Studies such as the studies [39,40,61] highlight the effectiveness of mathematical models, especially those based on column generation, multi-commodity network flows, and integer programming. However, these approaches often assume the availability of centralized planning tools and ideal input data—conditions that are rarely met in the context of regional crew bases.

Conversely, studies by [37,49,51,52] offer valuable insights into the practical implementation of crew scheduling models under diverse operational and legal frameworks. These works emphasize the need to balance model optimality with real-world applicability, particularly in heterogeneous and resource-constrained environments. In contrast to the above, this study is tailored to the practical conditions of a regional crew base—specifically, the Crew Centre Česká Třebová—where the exchange of shifts is limited, planning tools (such as the KASO system) are unavailable, and shift rosters are constructed primarily using graphical methods and locally accessible data. In response to the conclusions of the study [40], who emphasize the importance of accounting for actual employee attendance rates and planning robustness, this paper proposes a crew roster explicitly adapted to such constraints.

The originality of the proposed approach lies in its focus on real idle times, effective working time balances, and informal constraints that standard optimization algorithms typically do not address. The roster model also integrates social considerations, such as the reduction in night work, minimizing overnight stays outside the home base, and ensuring a balanced work–life schedule. In this respect, it aligns with the direction taken in the studies [42,55], who stress the importance of fairness and sustainability in crew planning. The outcome of this research is a practical adaptation of validated methodological principles to a constrained operational environment. The resulting optimized crew roster demonstrates improvements in personnel efficiency, average shift length, and the balance between working and rest periods—achieved without the use of complex software systems, and while maintaining compliance with staffing and operational limits. Although several of the cited studies are more than three decades old, they are included due to their foundational role in the development of railway crew scheduling methodologies. These works established principles that remain relevant and continue to inform modern optimization models. Their inclusion is therefore intended not as a reliance on outdated approaches, but as a recognition of their lasting contribution to the field.

3. Methodology

The methodology for designing new crew shift rosters was developed under the operational conditions of the Train Crew Centre Česká Třebová. Due to the unavailability of the standard KASO software tool—commonly used within České dráhy (in short ČD) for roster planning—an alternative multi-step approach was adopted. The KASO (Comprehensive Automated Circulation System) software is an internal rostering and circulation planning tool used by České dráhy (ČD) for the design and optimization of crew and vehicle schedules. As a proprietary system operated centrally by the railway company, it is not accessible to regional crew depots without a dedicated licence and technical infrastructure. Therefore, in the context of the Česká Třebová crew depot, the proposed methodology relies on a custom graphical approach. This approach is based on graphical analysis of transport tasks and the principles of efficient scheduling. The methodology relies on the systematic identification and visualization of all relevant shifts, their optimization, and the subsequent construction of new shift cycles. The process emphasizes the reduction in non-productive activities, compliance with legal constraints, and improved operational flexibility. The objective of this methodology is to design a work organization system for train crews that enhances overall efficiency, reduces staffing requirements, and simultaneously improves working conditions for employees.

The methodological procedure for developing train crew rosters in this study is structured into seven consecutive steps that systematically guide the process from data collection to the formulation of the final roster proposal. To enhance clarity and understanding of the individual phases, the entire procedure is illustrated in Figure 1.

Step 1. Collection and structuring of input data

The first step in the development of new crew rosters involves a systematic collection and structuring of all relevant input data. The key outcome of this step is the creation of a comprehensive database of train services that require crew coverage, along with associated technological, legal, and operational parameters. The foundation consists of a consolidated list of train services—including train numbers, categories (for example regional trains or express trains), routes, departure and arrival times, origin and destination stations, and journey durations. These services are supplemented with technological data, such as sign-on/off times, preparation and completion activities, transfer times between services (so-called lead-in and follow-up times), and any requirements for unlocking station facilities or performing other support activities. Simultaneously, constraints derived from labour legislation—particularly the Labour Code and collective agreements—are integrated into the methodology. These include the maximum allowable shift duration (for example 12 h), minimum rest time between shifts (for example 11 h), requirements for rest days, the maximum number of consecutive workdays, and specific regulations for split shifts.

An essential part of this step is the consideration of crew qualification requirements, especially specialization for D3 railway lines, the validity of D-30 exams, and knowledge of local operational regulations. Based on these, it is determined which employees may be assigned to specific train services. The output of this step is a set of structured data that forms the basis for graphical analysis and roster proposal development. This phase is critical to ensuring the professional, efficient, and legally compliant design of the roster.

In addition to collecting operational and technological data, the integration of legal and contractual constraints (such as maximum shift duration, minimum rest periods, and limits on split shifts) forms an essential part of Step 1. This ensures that all subsequent phases of the rostering process are based on inputs that already comply with the applicable labour legislation and collective agreements, rather than relying solely on a later verification in Step 6.

Step 2. Optimization of Shifts—Construction of Candidate Shifts

The second step focuses on the optimization of train service assignments through the creation of candidate shifts. The goal is to assemble operationally feasible shift blocks that maximize the utilization of available work time while respecting all technical, legislative, and operational constraints. In constructing candidate shifts, time and location continuity between train services must be maintained, ensuring seamless transitions and minimizing non-productive times. Additionally, cyclic shifts are preferred to facilitate return to the Home Depot within the same day. All shift variants must comply with the established legal, operational, and technical boundaries, which are strictly enforced during this phase. The output is a set of optimized shift candidates serving as building blocks for the subsequent formation of full crew rosters. The maximum usable duration of a shift is calculated using Equation (1):

$$T_{max}=min(T_{legis},T_{operational}, T_{service}, T_{technical})$$

(1)

where

• T_legis—maximum shift duration permitted by labour law (for example 12 h);
• T_operational—feasible time span based on train schedules and return options;
• T_service—net time of train escorting or direct service;
• T_technical—times required for preparation, transfer between tasks, and shift closing activities.

Step 3. Design of Roster Days

The third step involves constructing individual roster days by systematically assigning the previously optimized candidate shifts into a cyclic roster structure. Each roster day must comply with both legal and operational constraints to ensure the feasibility and sustainability of the work plan. The key conditions that each roster day must satisfy are:

$$T_{rest\_period}\ge T_{min\_rest\_period}$$

$$T_{shift}\le T_{max\_shift}$$

where

• T_{rest_period}—the actual rest time between two consecutive shifts (from the end of one shift until the start of the next);
• T_{min_rest_period}—the minimum legally or contractually required rest period between shifts (for example 11 h according to the Labour Code);
• T_shift—average shift duration;
• T_{max_shift}—the maximum allowable duration of a work shift, as set by legislation or operational regulations (for example 12 h).

Roster design is guided by the need for cyclicity—meaning that the sequence of shifts should repeat after a defined period, most commonly a 5-day or 7-day cycle, depending on operational requirements and crew scheduling policies. The objective is to ensure a balanced distribution of workloads, adequate rest periods, and consistent rotation patterns throughout the cycle. This phase transforms optimized shift blocks into a structured shift roster while maintaining temporal logic, operational realism, and legislative compliance. The result is a set of roster days that collectively form the framework of the full crew schedule.

Step 4. Rosters Balancing

The balancing of shifts within the roster aims to maintain a low deviation, ensuring an even distribution of workload among crew members. The standard deviation is calculated using Formula (2):

$$\sigma =\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{(T_{{shift}_i}-{\overline{T}}_{shift})}^2}$$

(2)

where

• σ—standard deviation of shift durations in the roster;
• T_shifti—duration of the i-th shift;
• n—number of shifts.

Step 5. Elimination of Redundant Deadhead Trips

The share of deadhead trips (P_dh) is calculated using Formula (3):

$$P_{dh}={\displaystyle \frac{T_{dh}}{T_{shift}}}\times 100 \left[\%\right]$$

(3)

where

• P_dh—percentage of deadhead time;
• T_dh—total time spent on deadhead trips;
• T_shift—total shift time.

The goal of the optimization is to minimize P_dh, particularly by combining suitable train relations, planning transfers at meaningful interchange stations (for example Letovice–Brno–Modřice), and reallocating trains between Crew Workplaces in cases of excessive inefficiency.

Step 6. Legal and Regulatory Compliance Assessment

In this step, the proposed rosters are verified against all applicable legal and contractual requirements, particularly the provisions of the Labour Code, internal regulations of the railway operator [15], and the valid Company Collective Agreement. The assessment includes, for example,

• Whether the duration of any shift does not exceed the maximum legal limits (for example 12 h);
• Whether the legally required minimum rest period between shifts is observed (typically 11 h);
• Whether split shifts do not exceed the permitted number of split segments (a maximum of two per shift);
• Whether the minimum shift length (for example 6.5 h) complies with PKS regulations,
• Whether rest cycles are maintained, such as the minimum number of days off and their even distribution.

If any roster proposal fails to meet the requirements of the Company Collective Agreement or legal regulations, it is modified at this stage—for instance, by extending or shortening a shift, adding an extra shift, or reorganizing the circulation plan. The objective is to ensure that every shift day is fully compliant with all regulatory frameworks before being submitted for consultation and feedback.

Step 7. Finalization of the Proposal and Preparation for the Approval Process

Following the legal review and optimization, the finalization of the roster proposal is carried out. In this step, all rosters are compiled into their definitive form, with the assignment of specific shift days, rotation patterns, and identifiers.

Subsequently, output materials are prepared in the form of structured tables and graphical diagrams illustrating the sequence and timing of shifts. These outputs serve as the basis for internal presentations and professional discussions with employees, their representatives (roster delegates), and trade unions.

An integral part of this final phase is the assessment of the operational sustainability of the proposed rosters by the service allocation unit and the relevant supervising regional officer. Upon approval, the finalized roster proposal is formally submitted for validation no later than 30 days before the planned implementation date. This ensures sufficient time for feedback, adjustments, and eventual deployment into live operation.

Efficiency of the Proposed Roster:

The efficiency of the proposed roster is evaluated based on the employee utilization rate during a shift (η), which is calculated using Equation (4). The aim is to achieve a value as close as possible to 100%, with values above 80% considered highly efficient.

$$\eta ={\displaystyle \frac{T_{service}}{T_{total}}}\times 100 \left[\%\right]$$

(4)

where

• T_service—time during which the employee is actively accompanying a train (productive operational time);
• T_total—total time spent at work, including idle time, allowances, and operational-related activities.

The share of non-productive time (τ) is a key indicator aimed at minimizing unproductive periods—with an optimal target value below 20%. It is calculated using Equation (5):

$$\tau ={\displaystyle \frac{T_{non-productive}}{T_{total}}}\times 100 \left[\%\right]$$

(5)

where

• T_{non-productive}—time spent on idle periods, deadhead travel without escort shift, waiting, or breaks outside of designated rest periods;
• T_total—total time spent at work.

The Overnight Stay Index Outside the Home Depot (INN) aims to reduce the proportion of overnight stays away from the home base, where feasible (preferably through return by deadhead travel). It is calculated using Equation (6):

$$INN={\displaystyle \frac{N_{overnight}}{N_{shift}}}\times 100 \left[\%\right]$$

(6)

• N_overnight—number of shifts ending outside the home crew depot with required overnight rest;
• N_shift—total number of shifts during the monitored period.

The Split Shift Index (SSI) is calculated using Equation (7) and aims to maintain a low proportion of split shifts (e.g., <20%), unless justified by operational requirements.

$$SSI={\displaystyle \frac{N_{split}}{N_{shift}}}\times 100 \left[\%\right]$$

(7)

where

• N_split—number of shifts that include a split in working time (e.g., breaks longer than 1 h);
• N_shift—total number of shifts.

The Index of Shift Repetition (IDR) is used to ensure the stability and predictability of the roster by promoting repeated shifts. A minimum repetition rate of 50% is recommended.

$$IDR={\displaystyle \frac{N_{repeated\_shifts}}{N_{total\_shifts}}}\times 100 \left[\%\right]$$

(8)

where

• N_{repeated_shifts}—number of shifts that are repeated regularly (daily or weekly);
• N_{total_shifts}—total number of planned shifts in the roster.

The Index of Circulation Coherence (ICC) aims to increase the logical connectivity of shifts and minimize the need for non-productive repositioning runs. It is calculated using the following formula:

$$ICC={\displaystyle \frac{N_{logical\_turns}}{N_{total\_turns}}}\times 100 \left[\%\right]$$

(9)

where

• N_{logical_turns}—number of shifts where the transport task has a logical return connection (return train to the departure station);
• N_{total_turns}—total number of train circulations in the roster.

Calculation of Annual Turnus Cost for a Specific Shift Type

The total annual employer cost for implementing a given shift type is calculated using the following formula:

$$N=k\times \left[d\times (p_n\times s_n+p_d\times s_d+{ds}_n\times s_{dsn}+{ds}_d\times s_{dsd}+s_{2D})\right]+s\times d$$

(10)

where

• N—total annual personnel cost for the given shift type;
• k—employer cost coefficient (includes mandatory contributions and overheads);
• d—number of days per year the shift is operated;
• p_n—number of night work hours within the shift;
• s_n—hourly wage for night work (depending on day of the week);
• p_d—number of day work hours within the shift;
• s_d—hourly wage for day work (depending on day of the week);
• ds_n—length of night interruption in hours;
• s_dsn—hourly rate for night interruptions;
• ds_d—length of day interruption in hours;
• s_dsd—hourly rate for day interruptions;
• s_2D—additional allowance for two-day shifts (if applicable);
• s—per diem allowance for the given shift.

The process of designing new crew rosters within the ČD environment is typically carried out using specialized software tools, most notably the KASO system. The core of the applied methodology lies in the extraction of all train services assigned to the train crew centre Česká Třebová and the subsequent construction of new shift cycles, without relying on existing roster templates. The procedure adheres to applicable legal regulations and the principles of efficient crew workload planning. During the design of new rosters, particular emphasis is placed on

• Efficient workload distribution within a single shift;
• Minimization of split shifts, which are applied only in operationally justified cases;
• Elimination of unnecessary deadhead trips wherever feasible; for instance, the connection between Svitavy and Žďárec u Skutče presents limited possibilities;
• Removal of overnight stays outside the Home Depot during two-day shifts—such cases are resolved by assigning return deadhead trips, allowing the employee to report for shift at their home train crew centre the following morning.

The methodology also focuses on staff savings, which is expected to partially address the long-standing shortage of on-board personnel. This, in turn, creates space for more flexible and responsive allocation of shifts. A limiting factor of the proposed methodology is the lack of communication with the roster planner of regional office Brno, which significantly restricts the possibility of shift exchanges between individual regional office centres and reduces the overall efficiency of the proposed design. Consequently, the proposal is based on the current state of train operations within the train crew centre Česká Třebová and reflects conditions that are suboptimal from an operational standpoint. The underlying philosophy of the proposed methodology is to design new roster schemes regardless of train category, aiming to ensure the most balanced distribution of shifts—from both the employer’s and the employee’s perspective—and to create opportunities for more efficient deployment of human resources within the operational process.

Furthermore, it should be noted that the seven-step methodology was not implemented as a dedicated software tool. Instead, the rostering process was carried out through a graphical analysis supported by spreadsheet calculations and manual validation, reflecting the limited availability of specialized planning software.

4. Research Background

The organization of on-board service activities within passenger railway transport is governed by the internal regulation of the railway operator, designated as [15]. This regulation defines the principles of unified and effective work organization within the structure of regional passenger transport directorates, regional customer service departments, and their subordinate train crew centres. Its primary objective is to ensure efficient management, coordination, and supervision of the assignment of train crews to operational duties. ČD K 13 [15] sets out the rules for the allocation of duties to on-board personnel, the methodology for roster planning, and the principles for determining the optimal number of train crew members required for individual operational units. Furthermore, it defines key technical terms used in the planning and organization of rostered services, thereby establishing a standardized framework for practical applications in the field of human resource management in railway operations. Train crew centres represent operational units where train crews are concentrated for reasons of efficiency and rationalization. These centres are organizationally subordinated to designated service assignment departments, with each regional customer service department ensuring the operation of at least one such centre in a continuous (24/7) mode. In cases where other service assignment departments are not staffed, the continuously operating centre assumes their responsibilities, thus ensuring continuity of operational management and service support.

4.1. Preparatory Activities

The preparatory activities of train crews encompass a set of tasks performed prior to and following the main operational shift—namely, train escort—as well as tasks executed at the beginning, end, or during the shift. These activities are essential to ensure the smooth and safe operation of railway services and are closely linked to local operational conditions and train type. The time allocated for these tasks is referred to as preparatory time. The duration of preparatory activities depends on various factors, such as train composition, the number of carriages, the range of guaranteed services provided (supervised luggage transport), internal duties (regular transport of official consignments), and local technical-organizational conditions, including vehicle turnarounds and staff transfers between trains. The main preparatory activities carried out at the beginning of a shift include

• Reporting for shift—typically via the internal ČD Komunikátor application on the service mobile device; in case of technical issues, reporting may be carried out by telephone to the relevant service assignment office.
• Familiarization with operational documentation necessary for safe service execution—accessed electronically through the employee portal.
• Receiving the portable ticketing device including accessories (spare battery, payment terminal).
• Inspection of the technical condition of the train set.
• Preparation of train documentation, such as brake reports, rolling stock lists, and defect reports.
• Verification of correct train composition.
• Collection of official consignments.
• Marking of reserved seats and designated compartments, if not performed by another designated staff member or automated system.
• Operation of train equipment, such as heating, air conditioning, and lighting.
• Other activities specified by local internal regulations, in accordance with ČD K 13 [15].

4.2. Finalization Activities and Preparatory Time Intervals

Among the preparatory tasks carried out upon detachment from a train or prior to the end of a shift are activities focused on train handover and administrative closure of shift. Their purpose is to ensure the proper conclusion of escort service by train personnel, transfer of responsibility, and readiness of the train set for subsequent operations. These activities include

• Securing the stabling of the train set or its dispatch to a stabling yard;
• Handing over official consignments;
• Removal of seat reservation and designated compartment markings (if this process is not automated or performed by another staff member);
• Handover of the train set to another member of the train crew;
• Submission of collected fare revenue and return of the portable ticketing device and payment terminal;
• Execution of additional activities in accordance with local operational instructions;
• Reporting the end of shift to the dispatcher or service assignment office.

These activities form part of the preparatory time intervals, which, according to internal regulations, apply not only at the beginning of a shift but also at its conclusion. Preparatory time intervals represent the time blocks allocated for completing all necessary administrative and technical tasks related to escorting the train by crew members. Typically, they comprise the preparatory and finalization activities and are included in the total duration of the crew member’s shift.

4.3. Preparatory and Technical Time Intervals Prior to Train Departure

Preparatory and technical time intervals allocated to train crews before train departure are intended to ensure the execution of all necessary duties related to shift commencement, train preparation, and the fulfilment of operational tasks as prescribed by Regulation ČD K 13 [15]. The standard shift start time at the home train crew depot is set at 20 min for all categories of personnel. This is followed by a pre-departure technical interval, typically 5 min, although in the case of specific train configurations (locomotive-hauled services without carriages or electric/multiple units with varying numbers of cars), this interval ranges from 10 to 25 min, depending on the complexity of preparatory activities. For the labelling of reserved seats and designated compartments, additional time allocations are defined as follows:

• Five to fifteen minutes for trainsets with 2 to 5 coaches;
• Fifteen to thirty minutes for trainsets with 6 to 10 coaches, depending on whether the marking process is performed manually or partially automated.

In the case of on-axis crew changes (when a prepared trainset is handed over from one staff member to another), a standard time of 5 min is assumed regardless of the crew member’s role. Upon evaluation of specific local operating conditions, these preparatory times may be adjusted—either shortened or extended. Key factors considered in such adjustments include turnaround times, the technical complexity of the trainset, and the number of assigned crew members.

4.4. Preparatory and Technical Time Intervals After Train Arrival

Post-arrival activities performed by the train crew constitute an integral part of the overall working shift and are incorporated into the post-arrival preparatory and technical time intervals. The purpose of these intervals is to ensure the proper administrative and technical closure of shift, formal handover of the trainset, and completion of all necessary tasks prior to leaving the workplace.

The standard time allocated for shift termination at the home train crew depot is 15 min for all categories of personnel. The technical interval following train escort, i.e., the time reserved for tasks performed immediately after train arrival, is typically 5 min, though it may extend up to 15 min, depending on the type and configuration of the trainset. For trainsets composed solely of a locomotive, the interval is set at 5 min. For electric or diesel multiple units, the time varies based on the number of vehicles:

• Two to five coaches: 5 to 10 min;
• Six coaches: 10 to 15 min.

In the case of conventional trainsets, the interval ranges from 10 to 15 min, depending on the level of crew involvement. For on-axis crew changes following train arrival—where the trainset is handed over to another crew member without technical handling—a standard buffer of 5 min applies to all job categories. As with pre-departure operations, these time values may be adjusted according to local conditions, including infrastructure parameters, crew availability, and operational timetables.

4.5. Crew Shift Roster Development Process

Within the organizational framework of ČD, a shift roster represents a cyclically repeating sequence of vehicle or crew assignments that are systematically scheduled for specific operational tasks in railway service.

4.5.1. Circulation Planning

The planning of crew circulations is a long-term and continuous process that takes place throughout the year. The primary objective of this process is to ensure the staffing of train formations with on-board crew, based on specific rules and requirements defined in internal regulation ČD K 13. The total number of duties that require personnel coverage is determined by the transport contracting authority—typically a regional government in the case of regional passenger transport, or the state in the case of long-distance services. The contracting authority, in cooperation with the Regional Commercial Centre, defines the service plan requirements for the upcoming railway timetable period. These requirements are entered via the KASO–Train planning software and include details about rolling stock composition, staffing needs for train and locomotive crews, and any special service requirements (low-floor access, Wi-Fi availability, guaranteed connections, etc.). ČD subsequently prepares a draft schedule of duties, which is discussed and iteratively adjusted until a final approved version is reached.

The infrastructure manager (Správa železnic) is also involved in the process, particularly to ensure operationally feasible train paths and to resolve potential conflicts, especially on single-track lines. Thus, the circulation planning process occurs within a tripartite framework involving ČD, the infrastructure manager, and the contracting authority, ultimately resulting in an optimized set of train duties for the new timetable period.

The actual development of crew circulations is carried out by the crew scheduling technologist using the KASO–Client application, which is interconnected with the KASO–Train module. The working basis for circulation planning is typically prepared in a structured format (for example Excel), and the technologist aims to achieve maximum synchronization between trainset and crew circulations. This synchronization significantly reduces administrative workload (preparation of train documentation, brake sheets, rolling stock records) and alleviates physical strain on staff caused by carrying heavy service equipment. This planning approach enhances operational efficiency, minimizes unproductive movements (non-revenue repositioning trips), and improves scheduling of shifts and rest periods in compliance with legislative and collectively agreed limits.

Within the KASO–Client environment, each train is assigned a unique identification number. When the scheduling technologist modifies any parameter of a train—such as its timetable slot or another characteristic—the system automatically updates all related circulation diagrams that have already been generated. However, if such a change results in an operational conflict or inconsistency in the circulation logic, the system issues a warning and requires user intervention to resolve the issue.

The responsibility of the crew scheduling technologist is to design shift rosters in compliance with applicable regulations, which encompass not only the internal documentation of the railway operator but also binding legal norms such as the Labour Code, government regulations, and the company-level collective agreement. When developing crew schedules, it is essential to ensure the following:

• Maximization of line performance (effective utilization of time spent directly on the train route);
• Minimization of preparatory and non-productive activities, particularly deadhead movements (non-revenue trips not involving passenger escort);
• Logical sequencing of duties, especially with respect to trainset connections and turnarounds;
• Prevention of timetable disruptions;
• Adherence to maximum shift durations and statutory rest periods between duties, as prescribed by labour legislation.

A well-designed shift roster must therefore meet not only technical and operational requirements but also social and labour constraints, while contributing to the overall stability and efficiency of the railway service.

4.5.2. Construction of Shift Rosters from Individual Shifts

In the context of České dráhy a shift roster consists of a set of work shifts that are cyclically arranged into recurring shift sequences. Depending on the volume of duties and the organizational structure of the train crew depot, multiple independent rosters may exist—typically, for example, one for regional passenger services and another for long-distance services, as is the case in the Česká Třebová Train Crew Depot (Shift Roster AR2). In smaller or local depots, there is usually only one roster, generally dedicated to regional transport. A roster for long-distance services may exceptionally include train duties of a higher or lower service category—mainly for the sake of efficiency and rationalization of work shifts. The same principle applies to regional transport rosters, which may incorporate long-distance duties when justified. However, at least 75% of duties within a roster must correspond to the primary train category for which the roster is designated. Exceptions below this threshold require approval by the central management unit of the General Directorate of ČD.

This management unit is also responsible for ensuring the balanced assignment of train duties of all categories among individual depots, with an emphasis on minimizing staff numbers and reducing non-productive activities such as deadhead transfers or prolonged idle time. The number of roster days and the resulting staffing requirements are determined based on the volume of assigned duties and are automatically calculated in the KASO—Client system for each roster individually. The number of roster days must not be divisible by seven to avoid weekly repetition of the same shifts. A standard staffing reserve is set at 22%, which covers typical employee absences due to vacations, sick leave, or other operational reasons.

A shift roster may be characterized, in terms of working time over a 28-day period, as follows:

• Overloaded: if the total working time exceeds the standard of 144 h in 28 days.
• Underloaded: if it falls below this threshold.

Employees generally prefer overloaded rosters because they do not require the insertion of extra shifts outside the roster cycle. In contrast, underloaded rosters may necessitate additional shifts during rostered time off. Once the draft shift roster has been created by the crew scheduling specialist, it is submitted to the crew representative, who presents it to employees and collects their feedback. It is recommended that the draft roster be published with sufficient lead time. After incorporating employee comments, the proposal is sent to the Trade Department, the Regional Business Centre, and the Správa železnic at least 30 days prior to the intended implementation. The Regional Business Centre and the Infrastructure Manager must then provide their requirements for turnaround operations within 10 days. The final version of the shift roster must be formally approved no later than 14 days before its effective date.

4.6. Current Status of Rosters at the Train Crew Centre Česká Třebová

The Train Crew Centre in Česká Třebová is responsible for staffing passenger train services in both long-distance and regional transport. As of 2024, train crew centre Česká Třebová employed 50 train conductors under full-time contracts and 3 conductors under work agreements, all of whom were certified under the O-04 qualification (operation of passenger trains).

The crew at this centre also operates on railway lines governed by simplified traffic control (D3 lines). However, not all conductors hold the required qualification for D3 operations. Conducting duties on D3 lines requires successful completion of the D-30 exam (general knowledge of D3 line operations) as well as route-specific familiarity through the Operational Instruction for D3 Line. Due to the limited number of qualified conductors with a valid D-30 certificate, staff from other crew centres—most often from Pardubice—are temporarily assigned when shortages occur. This process is typically initiated by the shift assignment office, which reallocates a qualified employee from a less restrictive assignment. This leaves one service unstaffed, which may then be covered by personnel from another crew centre, provided they have the necessary route knowledge and agree to work away from their home base. This system enables flexible personnel management and reduces the risk of disruption in planned shift rotations.

Train services assigned to individual crew centres are allocated by the shift scheduling specialist responsible for a given geographic area. In the case of train crew centre Česká Třebová, this responsibility lies with a specialist based in Pardubice. Multiple scheduling specialists operate within ČD, and they maintain close communication and coordination—especially in situations where trains cross between different areas of responsibility. Such cooperation is critical during track maintenance or closures, which can influence roster structures—either temporarily or permanently. Short-term disruptions may result in provisional roster changes, while long-term or major works may lead to the reallocation of duties between crew centres. The total volume of train services (vehicle runs) assigned to all rosters within train crew centre Česká Třebová, in the context of the railway network managed by Správa železnic and the wider Czech railway network, is illustrated in Figure 2.

Analysis of Shift Roster AR2

Shift roster AR2 is structured as a long-distance passenger transport shift. Its primary operational axis is line R19 (Prague–Česká Třebová–Brno), whose services are commissioned by the state as long-distance operations. However, AR2 is a combined shift roster, where long-distance services are supplemented with regional operations commissioned by individual regional governments. These include the following lines and routes [64]:

• Line S2: local trains between Modřice–Brno main station–Letovice;
• Local trains on the Česká Třebová–Letovice route;
• Local trains on the Česká Třebová–Kolín route;
• Local trains on the Pardubice–Letovice route;
• Local trains on the Česká Třebová–Rudoltice v Čechách–Lanškroun route,
• Semi-fast trains of line S22: Choceň–Česká Třebová–Letovice.

The transport performance of the AR2 roster within the railway network administered by Správa železnic and the infrastructure of the Czech Republic is shown in Figure 3 and an analysis of shift roster AR2 is shown in

Table 1. Analysis of Shift Roster AR2.

Shift Day	Validity (Days)	Start	End	Shift Duration (h)	Rest Duration
AR2/1	Weekdays	4:16	17:30	13:14	9:48 (Mon–Thu), 10:56 (Fri)
AR2/1	Saturday	7:49	21:11	11:53	8:24
AR2/1	Sunday	7:23	18:08	9:22	9:05
AR2/2	Weekdays	3:13	12:34	7:58	22:56 (Mon–Thu), 18:49 (Fri)
AR2/2	Saturday	4:26	13:06	8:40	22:43
AR2/2	Sunday	5:35	12:08	6:33	23:22
AR2/3-4	Mon–Thu	11:30	12:08	15:38	2–3 days
AR2/3-4	Friday	11:30	10:19	15:08	2 days
AR2/3	Saturday	7:23	18:08	9:22	2 days
AR2/3-4	Sunday	11:49	10:08	15:19	2 days

.

Analysis of Shift Roster A4

Shift Roster A4 is structured as a schedule comprising exclusively of regional passenger services commissioned by regional self-governing authorities. Informally, it is considered a roster primarily intended for conductors residing in Česká Třebová or its immediate surroundings, due to frequent early shift start times. The scheduled train services included in this shift roster mainly cover the following regional passenger lines [65]:

• Regional trains on the Česká Třebová–Letovice line;
• Regional trains on the Česká Třebová–Rudoltice v Čechách–Lanškroun line;
• Regional trains on the Svitavy–Čachnov line;
• Regional trains on the Česká Třebová–Kolín line;
• Regional trains on the Česká Třebová–Moravská Třebová line.

The duties in shift roster A4 are supplemented with technological tasks and scheduled breaks in accordance with the collective agreement. These are primarily implemented to artificially extend the duration of shifts to meet the requirement for the minimum working time. The scope of the transport services included in shift roster A4, within the context of the railway network administered by the Railway Infrastructure Administration and the Czech Republic, is illustrated in Figure 4 and an analysis of shift roster A4 is shown in

Table 2. Analysis of Shift Roster A4.

Shift Day	Validity (Days)	Start	End	Shift Duration (h)	Rest Duration
A4/1	Weekdays	3:42	16:38	12:56	11:36 (Mon–Thu), Friday
A4/1	Weekend	3:38	11:06	7:28	17:46 (Sat), 17:08 (Sun)
A4/2	Weekdays	4:14	10:00	05:56	1 day
A4/2	Saturday	Free day	x	x	x
A4/2	Sunday	4:52	12:29	7:38	1 day
A4/3	Mon–Sun	Free day	x	x	x
A4/4	Weekdays	3:38	11:06	7:28	24:30 (Mon–Thu), 29:31 (Fri)
A4/4	Weekend	Free day	x	x	x
A4/5	Weekdays	12:36	23:21	9:34	12:12
A4/5	Weekend	16:37	23:52	7:15	11:41
A4/6	Weekdays	11:33	23:16	10:22	2 days
A4/6	Saturday	11:33	23:16	9:58	2 days
A4/6	Sunday	11:33	22:15	8:54	2 days
A4/7	Mon–Sun	Free day	x	x	x
A4/8	Mon–Sun	Free day	x	x	x

.

Analysis of Shift Roster A5

Shift roster A5 represents the work cycle of train crew personnel exclusively within regional passenger transport, which is commissioned by individual regional authorities. Within the area of the Train Crew Centre Česká Třebová, it is the larger of the two rosters focused on regional passenger services. The following train services are included in the duties of this roster [66]:

• Local passenger trains on the Svitavy–Čachnov–Žďárec u Skutče route;
• Local passenger trains on the Česká Třebová–Rudoltice v Čechách–Zábřeh na Moravě route;
• Local passenger trains on the Česká Třebová–Kolín route;
• Local passenger trains on the Česká Třebová–Moravská Třebová route;
• Local passenger trains on the Česká Třebová–Rudoltice v Čechách–Lanškroun route;
• Local passenger trains on the Česká Třebová–Letovice route;
• Semi-fast trains on the Česká Třebová–Letovice route.

In addition to the standard train duties, roster A5 also includes technological tasks and so-called scheduled breaks according to the Company Collective Agreement, which are primarily intended to artificially extend the length of the shift to meet the minimum working time requirements stipulated by applicable regulations. The overall transport performance executed within shift roster A5 is illustrated in Figure 5, in the context of the railway network managed by the Railway Infrastructure Administration of the Czech Republic, and an analysis of shift roster A5 is shown in

Table 3. Analysis of Shift Roster A5.

Shift Day	Validity (Days)	Start	End	Shift Duration (h)	Rest Duration
A5/1-2	Mon–Thu	10:46	12:29 (+1)	18:40	11:03
A5/1-2	Friday	10:46	12:29 (+1)	18:35	11:08
A5/1-2	Saturday	11:35	10:11 (+1)	14:56	17:40
A5/1-2	Sunday	11:35	12:29 (+1)	17:35	17:19
A5/3	Weekdays	03:48	18:19	12:38	12:00
A5/3	Saturday	09:34	22:03	12:29	12:00
A5/3	Sunday	09:29	22:03	12:34	12:00
A5/4	Weekdays	12:21	21:11	8:50	12:00
A5/4	Saturday	04:27	11:27	7:00	24:00
A5/4	Sunday	x	x	x	x
A5/5	Mon–Sun	x	x	x	x
A5/6	Mon–Sun	x	x	x	x
A5/7	Weekdays	05:13	18:09	12:56	12:00
A5/7	Weekend	x	x	x	x
A5/8	Weekdays	04:18	16:13	11:55	12:00
A5/8	Saturday	10:36	22:15	9:40	12:12
A5/8	Sunday	12:46	21:11	8:25	12:12
A5/9-10	Mon–Thu	12:26	11:07 (+1)	14:30	9:00
A5/9-10	Friday	12:26	14:29 (+1)	17:03	9:00
A5/9-10	Saturday	12:46	14:29 (+1)	17:04	9:00
A5/9-10	Sunday	10:36	11:07 (+1)	16:20	9:00

.

The analysis of shift rosters was conducted using a combined approach that includes a detailed examination of individual variants of work shift sequences (shift days) and a graphical interpretation of transport performances. This approach enables a comprehensive evaluation of the temporal distribution of workload, efficiency of working time utilization, and identification of operational shortcomings in shift roster organization. The results of the analysis serve as a basis for optimization proposals aimed at improving the planning of shift shifts, considering both operational requirements and the legislative and social aspects of train crew work.

4.7. Weaknesses of the Current Rosters

Based on the shift roster analysis, one of the main weaknesses identified is the pronounced fragmentation of transport duties. This issue is primarily caused by the division of responsibilities between roster planners at the regional offices in Pardubice and Brno. As a result, transport services that are physically located within the operational scope of the Brno workplace are inappropriately assigned to train crew members from Pardubice, specifically from the Train Crew Centre Česká Třebová, without logical sequence continuity. An example is the operation of a local train on the Letovice–Modřice route, after which no return service follows, requiring the employee to return via a deadhead (non-revenue) trip. Similar cases are observed particularly in rosters AR2 and A5. This situation is also associated with a lack of coherence and uneven distribution of transport operations on individual routes and connections. Such an imbalance manifests in train crew exchanges at intermediate stations or in the excessive use of deadhead movements.

Another consequence is the significant difference in the volume of duties between weekdays and weekends, which negatively affects the structure and course of shift shifts—this is particularly evident in roster AR2. Consultations with the roster planner from the Pardubice office confirmed that these problems are due to insufficient and unbalanced communication between planners from different workplaces, as well as a general reluctance to engage in systematic negotiations concerning the redistribution of duties across routes and regions. According to his statement, this situation stems from a historically rooted belief in the “untouchability” of the train shift axes traditionally assigned to specific planning offices.

Another notable shortcoming identified is the relatively high proportion of split shifts. This phenomenon is rare in the European context and occurs almost exclusively in the Czech Republic (and historically in Slovakia). Split shifts were originally introduced as a compromise between the employer and trade unions to avoid dividing shifts into several short segments in situations where legal limits would otherwise prevent a feasible scheduling solution. However, over time, their application has expanded to include cases where their use is not strictly necessary. This issue is mostly pronounced in roster AR2 but also appears in other rosters. The main disadvantage is that the break period during split shifts is not counted as part of the working time fund. As a result, it leads to uneven workload distribution among employees and inefficient use of working hours.

Based on a visual and analytical interpretation of transport performances, the redundancy of a two-day shift with overnight accommodation in Letovice was also identified. It was found that this shift can be substituted by a non-revenue (deadhead) trip, thus eliminating the need for providing overnight rest facilities. Although the operator’s philosophy is to minimize the use of deadhead trips, in this case, their application would represent a justified exception in terms of operational efficiency.

5. Results

The new shift schedule has been developed based on the proposed methodology. The original roster plans were broken down into individual train services staffed by train crews, which were subsequently plotted in a graphical representation of transport operations. This visualization served as a foundation for identifying patterns and constructing new crew rotations. The proposed schedule encompasses the complete set of transport duties assigned to the Train Crew Depot in Česká Třebová. It represents a mixed roster, comprising both regional and long-distance passenger services. Conceptually, the schedule is designed as an “overperforming” roster, yet it fully respects legislative limits on annual working hours. This ensures that it does not require written employee consent for overtime work. The roster spans 41 days, which—compared to the existing slightly overperforming roster-reduces personnel demand by two employees. The outcome of the proposed solution is a shift schedule in the form of a weekly shift plan of the shift days (SD), illustrated in Figure 6 and Figure 7.

The proposal exceeds the minimum statutory working time fund (144 h per 28-day period), reaching an average of 155 h and 28 min, which corresponds to one shift of overtime. In accordance with applicable labour legislation, the employer may impose up to 150 h of overtime per year without the employee’s consent. Assuming a 52-week shift cycle, the minimum annual working time fund within the ČD environment equals 1874 h and 36 min. By adding the statutory limit of non-consensual overtime, the maximum permitted working time increases to 2024 h and 36 min.

The total time requirement of the proposed shift schedule over the 52-week horizon amounts to 2020 h and 58 min, creating a reserve of 3 h and 38 min. This buffer ensures compliance with legal restrictions and provides flexibility for unforeseen operational needs. The weekly shift schedule (illustrated in Figure 6 and Figure 7) presents a clear overview of working days and rest days within each week, as well as on a monthly or annual basis. It also serves as a foundation for calculating total working hours over weekly, 28-day, and annual cycles.

The structure of the new train crew rotations is designed starting from the most complex transport duties, where current conditions offer minimal opportunities for efficient staff allocation. A typical example includes regional passenger trains on the Svitavy–Žďárec u Skutče route. Emphasis is placed on the efficient creation of two-day shifts and ensuring adequate rest periods between them. In the analyzed environment, these include primarily two-day shifts with overnight rest or night split shifts at stations such as Polička, Borová u Poličky, Zábřeh na Moravě, and Březová nad Svitavou. The two-day shift with overnight accommodation in Letovice was evaluated as unnecessary and is proposed for cancellation.

After designing the two-day shifts, the development of one-day shifts followed, with both start and end located in the home base train crew centre. All new rotations are visually distinguished by colours. Each individual shift is assigned a unique colour, which is also used in the shift rosters. The graphical representation of rotations on a raster base is illustrated as an example in Figure 8 for a weekday, Figure 9 for Saturday, and Figure 10 for Sunday. In this way, all shift courses were recorded until full coverage of all transport services was achieved. After documenting the shifts, the final compilation into a complete shift schedule followed. Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 provide a detailed visualization of the crew rostering outcomes. Figure 6 and Figure 7 illustrate the baseline rosters, while Figure 8, Figure 9 and Figure 10 present the proposed optimized variants. In these graphs, colours distinguish individual shifts within the weekly cycle, nodes represent key train stations or crew change points, and the connecting paths indicate train services or deadhead movements. This graphical representation highlights the sequence and duration of duties, the temporal and spatial structure of crew work, and the reduction in idle time in the proposed rosters. By offering a clear colour-coded overview, the figures enable an immediate visual comparison between the existing and newly designed schedules and underscore the continuity and efficiency of the proposed roster. The schedule was created regarding legislative constraints, especially the maximum shift length, required rest intervals, and the weekly working time fund of 36 h (with permitted tolerance). Additionally, the plan includes a system for assigning scheduled days off. The resulting shift schedule includes a chronological sequence of individual shifts and rest days, as well as a weekly shift distribution table. This output forms the basis for further evaluation of the operational and personnel efficiency of the new proposal.

As part of the proposed methodology, the calculation of costs for the implementation of the actual transport work within the shift schedule considers the inevitably chargeable wage costs of the train crew members who will be involved in providing the service over the course of one calendar year.

The methodology does not account for the specific assignment of individual employees within the shift rosters, as in real operational conditions various personnel changes may occur—such as temporary transfers of employees to another train crew centre, sick leaves, or assignment to ad hoc shifts according to current operational needs. Additionally, equalization periods, which are typically carried out every three months, must be considered as they influence the planning and utilization of employees’ working hours. This flexibility in staff deployment enables more responsive operational management of transport services but also requires an accurate cost estimate for personnel regardless of their specific name-based assignment within the shift schedule. For calculating wage costs associated with the implementation of the shift roster, unit rates are used based on the type of wage, time of day (day/night), and days of the week (weekday/weekend). Hourly rates are also differentiated depending on whether the work is carried out during a standard shift or an extended (split) shift. An overview of the rates is presented in

Table 4. Wage rates for the calculation of shift schedule implementation costs (in €).

Wage Type	Applies to	Weekday	Weekend	Night (Weekday)	Night (Weekend)
ČD hourly wage	standard	€7.88	€9.07	€8.91	€10.09
ČD DS hourly wage	Long-shift roster	€3.94	€4.53	€4.45	€5.05

.

Based on the described methodology, the total wage costs for the implementation of the new shift schedule proposal for the year 2024 were calculated to amount to €915,901.57. For comparison, using the same calculation assumptions, the current shift schedules result in the following financial costs:

• Shift schedule AR2: € 303,756.77;
• Shift schedule A4: € 170,309.11;
• Shift schedule A5: € 392,994.75;
• Total cost of current shift schedules: € 867,060.72.

The comparison shows that the costs of implementing the current shift schedules are € 48,840.85 lower than the costs associated with implementing the proposed new schedule. This fact represents a significant factor in the decision-making process regarding the implementation of the new proposal. It is necessary to assess whether the increased costs are balanced by the expected operational, organizational, or personnel-related benefits, such as the reduction in required staff, elimination of two-day service shifts with overnight stays, reduction in split shifts, or improvement in the efficiency of shift planning.

6. Discussion

The new shift schedule proposal is based on a cycle consisting of 41 shift days, which will repeat approximately 8.88 times over the course of a calendar year. Out of the total 41 days, 26 are designated as working days and 15 as rest days, excluding rest periods embedded within working days (in weekend variants). Shift schedule AR2 is designed for a cycle of 15 shift days, with 10 working days and 5 rest days, again not accounting for hidden rest days within weekend variants. Schedule A4 is structured into 8 shift days, including 5 working days and 3 rest days. Schedule A5 consists of 20 shift days, with 13 working days and 7 rest days, excluding hidden rest days in certain weekend versions. From these figures, it is evident that the proposed new shift schedule is more efficient resulting in a reduction of two employees compared to the current shift schedules. Additionally, the new proposal features a more favourable distribution of work and rest days for the employee, as the same number of 15 rest days per cycle is maintained while reducing the number of working days by two.

Based on the arithmetic average of all planned service variants, the average shift duration in the new proposal is set at 9 h and 42 min. In contrast, the average shift duration in schedules AR2 and A5 was calculated at 8 h and 54 min, and in schedule A4 at 8 h and 44 min. This comparison shows that the proposed new schedule offers a longer average daily shift time than any of the existing schedules, as well as their collective average. This indicates a more efficient utilization of employees’ working time on the train. A graphical comparison of the average shift durations across the individual shift schedules is shown in Figure 11.

Due to the exclusion of break time during split shifts from the official working time fund, train crew members spend additional unaccounted time at work, which is not compensated for under the standard time allocation. For this reason, the new roster proposal incorporates split shifts only where strictly necessary—primarily to extend the duration of a shift that would otherwise have to be split into two shorter shifts. Under the new roster, a total of 3523 h and 5 min of break time is planned annually. For comparison, the annual break durations under the current rosters are as follows:

• Roster AR2: 1568 h and 9 min
• Roster A4: 847 h and 28 min
• Roster A5: 1499 h and 14 min.

Altogether, the current rosters account for a total of 3907 h and 51 min of service interruption per year. A comparison with the new roster proposal reveals a reduction of 384 h and 46 min, representing a significant decrease in non-productive employee workload and an overall improvement in work time organization efficiency. The analysis and subsequent proposal also confirmed that deadhead (non-revenue) trips cannot be eliminated, as they are essential for the transport of train crew to and from Svitavy station for regional services on the Svitavy–Žďárec u Skutče route, which cannot be staffed otherwise.

In fact, new deadhead trips were introduced in the proposed roster, specifically to eliminate one two-day shift with overnight accommodation in Letovice. Given the lack of possibilities for shift exchanges with other crew centres and the fact that the new proposal is constructed solely based on currently assigned transport services, there is no room for meaningful or systemic reduction in deadhead trips. Thus, deadhead trips remain an operational necessity, particularly for ensuring service coverage on less accessible lines, and they help reduce the reliance on more demanding rosters requiring external accommodation. The most notable idle times were identified at Brno main station, occurring between turns of trains on line R19. In current rosters, these idle times are typically filled with service interruptions, whereas in the new proposal, such interruptions are largely omitted. If cooperation with the train crew centre Brno centre were possible, employees from Česká Třebová could perform “direct turnarounds” by covering suburban services under the South Moravian Integrated Transport System (IDS JMK). However, due to existing limitations in inter-centre coordination, this possibility could not be included in the proposed roster. Additional idle times were identified in Česká Třebová and its vicinity, especially during the morning off-peak periods (so-called traffic troughs). Because these time slots naturally coincide with a low volume of train operations, there are no feasible opportunities to fill them with train services or meaningful auxiliary duties. Therefore, these time periods remain unutilized from the perspective of active work performance.

Despite the positive outcomes of the new roster proposal—including the reduction in staffing requirements, improved efficiency in the utilization of working time, and a more favourable distribution of work and rest days—it is essential to also pay attention to the practical aspects of its implementation in real-world operations. Implementing such a proposal may involve several risks that could affect the success of its application. Among the key implementation risks is the potential resistance of employees to changes, particularly regarding modifications to the split-shift regime and the increase in the average duration of shift. Another challenge is the current unpreparedness of planning tools—the workplace does not yet have access to modern systems such as the KASO planning software, which hinders efficient scheduling and updating of rosters. Equally important is the limited coordination between individual train crew depots, which prevents a more effective interconnection of duties and crew rotations. For these reasons, it is recommended to take several steps prior to full implementation to mitigate risks and support the successful deployment of the proposal. The first step should be a pilot test of the new roster on a smaller group of employees or over a shorter period, to verify its practical feasibility and identify potential shortcomings. The implementation process should also include transparent communication with employees and their active involvement in the discussion, for example, through workshops, training sessions, or satisfaction surveys. At the same time, technical preparation should be conducted—either by adapting existing planning tools or by introducing new systems such as KASO, which would enable more flexible planning in the future.

The evaluation of the proposed roster highlights several notable strengths and weaknesses. Among its main advantages is the reduction in the required number of employees, which contributes to improved operational efficiency. The proposal also leads to a shortening of unproductive idle times, enhancing the overall utilization of working hours. Furthermore, it introduces a more favourable distribution of work and rest days, which positively influences employee well-being. A significant benefit is also the reduction in the number of night shifts and rest periods spent outside the Home Depot, thus improving the quality of work–life balance. However, the proposal is not without its drawbacks. The most prominent among them is the higher average duration of shift per shift, which may lead to increased fatigue and reduced job satisfaction. The proposal also requires the continued use of deadhead (non-revenue) trips, which, while operationally necessary, represent inefficiencies. Additionally, existing idle periods during off-peak hours remain unresolved, as they cannot yet be effectively filled with meaningful tasks or services. From the standpoint of optimizing the work of train crews, the new roster proposal clearly represents a step forward. Nevertheless, its successful implementation will demand a comprehensive approach—one that goes beyond operational considerations and adequately addresses the organizational and social dimensions of the transition process.

In contrast to advanced optimization techniques such as column generation [39,40] or fairness-oriented heuristics [42,55], the proposed graphical method is designed for environments where such complex tools are unavailable or impractical. While it does not introduce algorithmic novelty in the traditional sense, its contribution lies in adapting established rostering principles to the specific conditions of a regional crew depot with limited technological support and no possibility of inter-depot shift exchanges. This practical adaptation ensures compliance with legislation, reduces the need for overnight stays, and minimizes split shifts without requiring specialized software. Thus, the method bridges the gap between theoretically optimal approaches and their real-world applicability in resource-constrained operational settings.

While the study emphasizes sustainability through the reduction in idle time and the improvement of work–life balance, it does not provide quantifiable indicators of sustainability impacts, such as estimated reductions in CO₂ emissions or employee satisfaction surveys. Including such indicators in future research would provide a more comprehensive assessment of the broader environmental and social benefits of optimized crew rostering. For example, calculating energy savings from fewer deadhead trips or conducting surveys to evaluate improvements in employee well-being could significantly enrich the contribution of the study to the discourse on sustainable transport.

7. Conclusions

This study provides a detailed analysis of the current state of train crew rosters at the Train Crew Centre in Česká Třebová and proposes their optimization. The objective was to identify operational and organizational weaknesses of the existing rosters and subsequently design a new, more efficient rostering model. Based on a graphical analysis of transport operations and the application of a proprietary rostering methodology, a new roster proposal was developed that integrates duties from both long-distance and regional passenger services. The new roster demonstrates several advantages: more efficient allocation of working time, a reduced number of staff required for its implementation, higher average daily workload per employee, and a lower number of split shifts. Although the total annual wage costs of the proposed solution exceed those of the current rosters by €48,751.01, the proposal offers operational and personnel benefits that may positively influence the long-term stability of work performance and planning.

One limitation of the proposal is the current impossibility of redistributing transport duties between individual Train Crew Centres and regional workplaces, which could significantly improve the overall efficiency of the proposed solution. It is therefore recommended to enhance interdepartmental communication between rostering technologists, revise historical allocations of operating routes, and consider the implementation of centralized tools for coordinating crew rotations across regions. The proposed rostering methodology and its application to real-world data provide a relevant tool for optimizing staff deployment in passenger railway transport and can serve as a model for other regional centres within the ČD environment.

Although the seven-step methodology has proven to be logically consistent and well-adapted to the conditions of the Česká Třebová crew depot, its applicability to other depots or network configurations has not yet been tested. A recommended direction for future research is to conduct sensitivity analyses or inter-regional simulations to assess the robustness and transferability of the proposed approach. Such analyses would help determine to what extent the methodology can be generalized and applied in different operational environments, thereby strengthening its practical relevance for broader railway systems. Another important limitation of the current study is that the model does not account for stochastic factors such as crew absences or train delays, which can significantly affect real-world operations. To enhance the robustness of the results, future research should consider the application of Monte Carlo simulations or scenario-based robustness checks. These methods would allow the assessment of schedule stability under uncertainty and provide more reliable insights into the feasibility and resilience of the proposed rostering model.

The proposed roster has not yet been formally consulted with railway employees or tested through pilot implementation. However, consultations with train crew representatives are planned as part of the subsequent phase of the research to assess employee acceptance and identify potential adjustments. Such engagement will be essential to ensure not only operational feasibility but also the practical and social sustainability of the proposed scheduling approach.

The proposed roster represents a practical step forward in train service planning; however, further research should address the digitalization and automation of the entire process. In the future, integrating crew scheduling into a centralized planning system such as KASO appears promising, enabling more effective coordination between train crew centres and eliminating barriers to duty redistribution. Another direction involves predictive workload modelling and generating optimal rosters using machine learning methods, which could lead to more dynamic and adaptive planning systems. Importantly, improving rostering practices not only enhances operational performance but also supports broader goals of sustainable transport systems—by enabling more energy-efficient crew utilization, reducing unnecessary train movements, and improving social sustainability through fairer workload distribution and better work–life balance. Comparing applied methodologies with international practices, particularly in countries such as Germany, the Netherlands, and China, may help identify transferable innovations and further contribute to the development of a modern, data-driven, and sustainability-oriented work organization in railway operations.

Although the proposed methodology relies on a graphical analysis of transport operations, the concept of optimization mentioned in the title also opens the possibility for further research. A promising direction for future work is the formulation of an objective function together with a set of mathematical constraints that would enable the development of a more robust optimization model. Such a function could aim to minimize non-productive time, reduce the number of required staff, or balance workload distribution, while constraints would reflect legislative limits, operational requirements, and employee preferences. Incorporating these elements in future studies would strengthen the methodological framework and provide a closer alignment with advanced optimization techniques widely applied in railway crew scheduling research.