Railway Crew Scheduling Research Articles

Heuristic for Railway Crew Scheduling With Connectivity of Schedules

This paper addresses the crew scheduling for long-distance passenger train services. A heuristic with bin packing features is developed to generate repeatable crew schedules that satisfy the operational and crew allocation rules. By ensuring the connectivity of crew duties that can be repeated over periodic train schedules, a better estimate of the crew requirement in a region is also obtained. Further, the heuristic ensures a fair division of the total workload and creates long duty cycles, which also makes the process of cyclic rostering easier. The paper also presents an exact approach for crew scheduling using a combination of constraint programming and set covering formulations. The exact approach is not computationally viable for practical scale problem instances, but the heuristic generates good quality solutions (often very close to optimal) even on large data sets. We illustrate the approach on data from the Mumbai Division in Indian Railways and the computational results show that there is potential to reduce the total number of crew duties in the region by around 12%. The heuristic approach provides an efficient way to generate improved crew schedules every time there is a change in the train timetable.

Optimize railway crew scheduling by using modified bacterial foraging algorithm

With crew scheduling and Artificial Intelligence (AI) gaining attention in the past few years, there has been growing interest in algorithms that could effectively handle the crew scheduling problem (CSP) in railway transport. Despite AI becoming pervasive in most engineering domains, there is a lack of methods that can provide high-quality crew scheduling in the railway industry. To fill this gap, this study designs a railway crew scheduling model of mixed integer linear programming (MILP) problem utilizing the bacterial foraging algorithm (BFA) and evaluates the model's advantages and limitations. BFA is a novel class of biologically inspired stochastic global search methodology that is based on E. coli bacteria's foraging behavior. Using the Taiwan Railways dataset, we compare the performance of the proposed BFA-based method for railway crew scheduling optimization (BFARCSO) against two benchmark methods, the genetic algorithm (GA) and the particle swarm optimization algorithm (PSO) and showcase its advantages in terms of solution quality and computation time. Finally, a series of computational testing and validation highlights the efficiency and superiority of BFARCSO. It demonstrates that this approach significantly improves the large-scale railway crew scheduling problem over typical approaches, making it well-suited to practice real-time decision support in railway crew scheduling.

Using Machine Learning to Include Planners’ Preferences in Railway Crew Scheduling Optimization

In crew scheduling, optimization models can become complex when a large number of penalty terms is included in the objective function to take planners’ preferences into account. Planners’ preferences often include nonmonetary aspects for which both the mathematical formulation and the assignment of appropriate penalty costs can be difficult. We address this problem by using machine learning to learn and predict planners’ preferences. We train a random forest classifier on planner feedback regarding duties from their daily work in railway crew scheduling. Our data set contains over 16,000 duties that planners labeled as good or bad. The trained model predicts the probability that a duty is perceived as bad by the planners. We present a novel approach to replace the large construct of penalty terms in a crew scheduling optimization model by a single term that penalizes duties proportionally to the predicted probability of being assessed as unfavorable by a planner. By integrating this probability into the optimization model, we generate schedules that include more duties with preferred characteristics. We increase the mean planner acceptance probability by more than 12% while only facing a marginal increase in costs compared with the original approach that utilizes a set of multiple penalty terms. Our approach combines machine learning to detect complex patterns regarding favorable duty characteristics and optimization to create feasible and cost-efficient crew schedules. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.1196 .

A Lagrangian relaxation approach based on a time-space-state network for railway crew scheduling

The Crew Scheduling Problem (CSP) is an important and difficult problem in railway crew management. In this paper, we focus on the railway crew scheduling problem with time window constraints caused by meal break rules. To address these complex crew scheduling rules, we construct a Time-Space-State Network (TSSN), formulate the studied problem as an initial network flow model and a strengthened network flow model. By exploring the characteristics of the TSSN and the improved model, we develop an efficient algorithm based on Lagrangian relaxation to get a valid lower bound. The latter algorithm is combined with solving a set covering model to get a good quality upper bound solution for the studied CSP problem. We compare the performance of our Lagrangian relaxation approach with a commercial solver (CPLEX) and Column Generation (CG) on several real-world instances based of Chinese high-speed railways. The computational experiments show that our method can solve the railway CSP in a very short computation time compared to both CPLEX and CG, while obtaining (near-)optimal solutions for all instances. We thus propose an innovative efficient and effective approach to improve the railway CSP with meal break constraints.

Solution of Multi-Crew Depots Railway Crew Scheduling Problems: The Chinese High-Speed Railway Case

This paper presents a novel mathematical formulation in crew scheduling, considering real challenges most railway companies face such as roundtrip policy for crew members joining from different crew depots and stricter working time standards under a sustainable development strategy. In China, the crew scheduling is manually compiled by railway companies respectively, and the plan quality varies from person to person. An improved genetic algorithm is proposed to solve this large-scale combinatorial optimization problem. It repairs the infeasible gene fragments to optimize the search scope of the solution space and enhance the efficiency of GA. To investigate the algorithm’s efficiency, a real case study was employed. Results show that the proposed model and algorithm lead to considerable improvement compared to the original planning: (i) Compared with the classical metaheuristic algorithms (GA, PSO, TS), the improved genetic algorithm can reduce the objective value by 4.47%; and (ii) the optimized crew scheduling plan reduces three crew units and increases the average utilization of crew unit working time by 6.20% compared with the original plan.

On a Real-World Railway Crew Scheduling Problem

A railway company has to deal with many interrelated planning tasks. In this work we consider the Railway Crew Scheduling Problem (RCSP) for the Rail Cargo Austria (RCA), which is the largest railway company for freight transportation in Austria and one of the largest in Europe. The RCSP aims for determining the most efficient combination of shifts. For RCA’s purposes these are shifts for engine drivers. A shift consists of a sequence of consecutive scheduled trips of locomotives and tasks over a given period of time. Each trip must be covered by exactly one shift while operational, legal and labor constraints are satisfied. The RCSP is known to be difficult to solve and there exists a wide range of solution approaches resulting from many research activities. We present and investigate a matheuristic to tackle the RCSP. We use a breadth-first search construction heuristic and formulate a Set Partitioning Problem with the aim of minimizing the overall paid working time, while all RCA specific constraints are incorporated. Although schedule efficiency and employee satisfaction are in general conflicting, a cost-efficient schedule will not be implemented if it does not reach acceptance of the crew. In a computational study we evaluate the proposed approach on it’s practical applicability on real-world data provided by RCA, based on the Austrian railway network. The focus is on analyzing the effects of different conditions on crew schedules. In the course of this evaluation we make use of algorithms from previous work on the Locomotive Scheduling Problem (LSP), tailored to RCA’s demands. The LSP is concerned with assigning locomotives to a train schedule while costs are minimized, and the obtained optimal locomotive schedule forms the input for the RCSP. This work provides the basis for a succeeding planning tool, as soon as the locomotive schedule was determined.

A novel model and solution algorithm to improve crew scheduling in railway transportation: A real world case study

This paper presents a novel mathematical formulation in railway crew scheduling, considering real challenges most European passenger railway companies face like roundtrip policy for crew members joining from different cities and stricter working time standards. To solve the problem in large scales of data (consistent with the real case size of the planning problems solved by rail transport companies), a solution algorithm is proposed. The algorithm includes two steps: I. Duty generation: pre-calculations to obtain all duties meeting the related constraints; II. Duty assignment: running the optimization model to select an optimal set of duties while satisfying other constraints. To investigate the algorithm’s efficiency, numerical test instances and a real case study have been employed. In addition, the savings that an implementation of the proposed approach allows to achieve instead of the manually prepared plans still applied in a lot of transportation companies are demonstrated. Results show that the proposed model and algorithm lead to considerable improvement compared to the original planning.

An efficient column generation approach for practical railway crew scheduling with attendance rates

The crew scheduling problem with attendance rates is highly relevant for regional passenger rail transport in Germany. Its major characteristic is that only a certain percentage of trains have to be covered by crew members or conductors, causing a significant increase in complexity. Despite being commonly found in regional transport networks, discussions regarding this issue remain relatively rare in the literature. We propose a novel hybrid column generation approach for a real-world problem in railway passenger transport. To the best of our knowledge, several realistic requirements that are necessary for successful application of generated schedules in practice have been integrated for the first time in this study. A mixed integer programming model is used to solve the master problem, whereas a genetic algorithm is applied for the pricing problem. Several improvement strategies are applied to accelerate the solution process; these strategies are analyzed in detail and are exemplified. The effectiveness of the proposed algorithm is proven by a comprehensive computational study using real-world instances, which are made publicly available. Further we provide real optimality gaps on average less than 10 % based on lower bounds generated by solving an arc flow formulation. The developed approach is successfully used in practice by DB Regio AG.

Railway crew scheduling with semi-flexible timetables

We investigate the impact of coordinating the timetable and the crew schedule in an operational freight railway system. Usually, those problems are solved sequentially—resulting in suboptimal schedules for train drivers due to large idle times between two train rides. We seek to coordinate the timetable and the crew schedule on the operational level by adding flexibility to the timetable. We introduce small time windows that allow to shift entire trains forwards and backwards by discrete time periods. We present a mathematical model and solve it with a column generation heuristic. We test our model on three real datasets of a major European Freight Railway Operator and show that significant reduction in idle time and cost can be achieved.

Efficient Railway Crew Scheduling in German Regional Passenger Transport

SINCE THE GERMAN RAILWAY REFORM IN 1996, federal states and transport associations are responsible for regional rail passenger transport. Usually, transport associations determine lines and timetab...

Railway Crew Scheduling Based on Step by Step Optimization and Graph Partitioning

Railway Crew Scheduling Based on Step by Step Optimization and Graph Partitioning

Railway crew scheduling in passenger transportation – optimization approach

Railway crew scheduling in passenger transportation – optimization approach

Two Mathematical Models for Railway Crew Scheduling Problem

Two Mathematical Models for Railway Crew Scheduling Problem

Solving Practical Railway Crew Scheduling Problems with Attendance Rates

Arising from a practical problem in German rail passenger transport, a prototype for a multi-period railway crew scheduling problem with attendance rates for conductors is developed and evaluated in this paper. The consideration of attendance rates is of increasing importance in regional transport networks and requires decision support. For this purpose business analytics is applied in order to offer an approach to transform real-world data to concrete operational decision support (action). The focus here is on the analysis step using a new set covering model with several essential restrictions integrated for the first time. A hybrid column generation approach is applied, which solves the pricing problem by means of a genetic algorithm. The artifact is evaluated with the help of a case study of three real-world transport networks. It is shown that the hybrid solution approach is able to solve the problem more effectively and efficiently compared to conventional approaches used in practice.

Optimizing railway crew schedules with fairness preferences

Railway crew scheduling deals with generating duties for train drivers to cover all train movements of a given timetable while taking into account a set of work regulations. The objective is to minimize the overall costs associated with a crew schedule, which includes workforce costs and hotel costs. A cost minimal schedule often contains duties that are unpopular to train drivers, and these unpopular duties are often unevenly distributed among crew depots. At the company that motivated our research, for example, train drivers dislike duties that start in the early morning hours. Currently, some crew depots operate large numbers of these unpopular duties, while others do not have any unpopular duties at all. The train drivers perceive this situation as unfair. They prefer schedules with fewer and more evenly distributed unpopular duties across crew depots. In this paper, we define and measure unpopularity and (un)fairness in a railway crew scheduling context. We integrate fairness conditions into a column generation-based solution algorithm and analyze the effect of increased fairness on cost. We also show how increased fairness affects the unpopularity of a schedule. Our method has been applied to test instances at a large European railway freight carrier. Compared to a standard approach that penalizes only the number of unpopular duties in a schedule, we were able to significantly improve schedule fairness with only marginal increases in schedule cost.

MODELLING AND OPTIMISATION OF RAILWAY CREW SCHEDULING

This research develops optimisation models and algorithms for railway crew scheduling problem (CSP). The scheduling criterion is to minimise the number of crew duties by reducing idle transition times while taking into account a complex set of railway crew scheduling related constraints. The integration of relief opportunities period (ROP) into the models and algorithms would enable the train crew to be relieved at any relief point within the time period of relief opportunities. This will enhance the robustness of the schedule and provide a better representation of real railway crew scheduling conditions. The models and algorithms are general and can be easily adapted to different locations and modes of transportation. Furthermore, the proposed models and algorithms can be extended to the integration of vehicle and CSPs with ROP.

A graph partitioning strategy for solving large-scale crew scheduling problems

Railway crew scheduling deals with generating driver duties for a given train timetable such that all work regulations are met and the resulting schedule has minimal cost. Typical problem instances in the freight railway industry require the generation of duties for thousands of drivers operating tens of thousands of trains per week. Due to short runtime requirements, common solution approaches decompose the optimization problem into smaller subproblems that are solved separately. Several studies have shown that the way of decomposing the problem significantly affects the solution quality. An overall best decomposition strategy for a freight railway crew scheduling problem, though, is not known. In this paper, we present general considerations on when to assign two scheduled train movements to separate subproblems (and when to rather assign them to the same subproblem) and deduct a graph partitioning based decomposition algorithm with several variations. Using a set of real-world problem instances from a major European railway freight carrier, we evaluate our strategy and benchmark the performance of the decomposition algorithm both against a common non-decomposition algorithm and a lower bound on the optimal solution schedule. The test runs show that our decomposition algorithm is capable of producing high-quality solution schedules while significantly cutting runtimes compared to the non-decomposition solution algorithm. We are following a "greenfield" approach, where no information on previous schedules is needed. Hence, our approach is applicable to any railway crew scheduling setting, including network enlargement, integration of new customers, etc.

A hybrid constructive heuristic and simulated annealing for railway crew scheduling

Railway crew scheduling problem is the process of allocating train services to the crew duties based on the published train timetable while satisfying operational and contractual requirements. The problem is restricted by many constraints and it belongs to the class of NP-hard. In this paper, we develop a mathematical model for railway crew scheduling with the aim of minimising the number of crew duties by reducing idle transition times. Duties are generated by arranging scheduled trips over a set of duties and sequentially ordering the set of trips within each of duties. The optimisation model includes the time period of relief opportunities within which a train crew can be relieved at any relief point. Existing models and algorithms usually only consider relieving a crew at the beginning of the interval of relief opportunities which may be impractical. This model involves a large number of decision variables and constraints, and therefore a hybrid constructive heuristic with the simulated annealing search algorithm is applied to yield an optimal or near-optimal schedule. The performance of the proposed algorithms is evaluated by applying computational experiments on randomly generated test instances. The results show that the proposed approaches obtain near-optimal solutions in a reasonable computational time for large-sized problems.

Divide-and-price: A decomposition algorithm for solving large railway crew scheduling problems

The railway crew scheduling problem consists of generating crew duties to operate trains at minimal cost, while meeting all work regulations and operational requirements. Typically, a railway operation uses tens of thousands of train movements (trips) and requires thousands of crew members to be assigned to these trips. Despite the large size of the problem, crew schedules need to be generated in short time, because large parts of the train schedule are not finalized until few days before operation.We present a column generation based decomposition algorithm which achieves high-quality solutions at reasonable runtimes. Our divide-and-price algorithm decomposes the problem into overlapping regions which are optimized in parallel. A trip belonging to several regions is initially assigned to one region (“divide”). The corresponding dual information from optimization is then used as a bonus to offer the trip to other regions (“price”). Pricing and assignment of trips are dynamically updated in the course of the optimization. Tests of our algorithm on large-scale problem instances of a major European freight railway carrier yielded promising results.

Divide-and-Price: A Decomposition Algorithm for Solving Large Railway Crew Scheduling Problems

Abstract The railway crew scheduling problem consists of generating crew duties to operate trains at minimal cost, while meeting all work regulations and operational requirements. Typically, a railway operation uses tens of thousands of train movements (trips) and requires thousands of crew members to be assigned to these trips. Despite the large size of the problem, crew schedules need to be generated in short time, because large parts of the train schedule are not finalized until few days before operation. We present a column generation based decomposition algorithm which achieves high-quality solutions at reasonable runtimes. Our divide-and-price algorithm decomposes the problem into overlapping regions which are optimized in parallel. A trip belonging to several regions is initially assigned to one region (“divide”). The corresponding dual information from optimization is then used as a bonus to offer the trip to other regions (“price”). Pricing and assignment of trips are dynamically updated in the course of the optimization. Tests of our algorithm on large-scale problem instances of a major European freight railway carrier yielded promising results.