Railway Crew Scheduling Problem Research Articles

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.

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.

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.

Column generation with dual inequalities for railway crew scheduling problems

The railway crew scheduling problem is to determine an optimal crew assignment for the railway timetable data by minimizing the required number of crew members in order to satisfy the set covering constraints. Column generation is one of the optimization methods that can solve the problem efficiently. In order to improve the convergence of column generation, we propose dual inequalities for a Dantzig-Wolfe decomposition of railway crew scheduling problems to reduce the number of replications in the column generation procedure. The dual inequalities are generated from the characteristic of the given railway timetable data. Computational results demonstrate the effectiveness of the proposed method compared with the conventional column generation for an actual railway timetable data.

実乗務制約を有する鉄道乗務員運用計画問題に対する列生成法の適用

実乗務制約を有する鉄道乗務員運用計画問題に対する列生成法の適用

Improvement of Column Generation Method for Railway Crew Scheduling Problems

The railway crew scheduling problem is to determine the assignment of crews to each traveling task to minimize the number of crews satisfying set covering constraints. Column generation method is often applied to solve railway crew scheduling problems. In this paper, we propose dual inequalities for railway crew scheduling problems to reduce the number of iterations in the column generation method. Three types of dual inequalities are generated from railway timetable data and they are added to the restricted master problem. Computational results show the effectiveness of the proposed method compared with the conventional column generation method.

An Application of Wedelin's Method to Railway Crew Scheduling Problem

So many scheduling problems arise in railway industries. One of the typical scheduling problems is Crew Scheduling Problem. Much attention has been paid to this problem by a lot of researchers, but many studies have not been done to the problems in railway industries in Japan. In this paper, we consider a railway crew scheduling problem in Japan. The problem can be formulated into Set Covering Problem (SCP). In SCP, a row corresponds to a trip representing a minimal task and a column corresponds to a pairing representing a sequence of trips performed by a certain crew. Many algorithms have been developed and proposed for it. On the other hand, in practical use, it is important to investigate how these algorithms behave and work on a certain problem. Therefore, we focus on Wedelin's algorithm, which is based on Lagrange relaxation and is known as one of the high performance algorithms for SCP, and mainly examine the basic idea of this algorithm. Furthermore, we show effectiveness of this procedure through computational experiments on instances from Japanese railway.

Parallel Integer Optimization for Crew Scheduling

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, Goteborg, Sweden, based on distributing the variables. A lazy variant of this approach which decouples communication and computation is even useful on networks of workstations. Furthermore, we develop a new sequential active set strategy which requires less work and is better adapted to the memory hierarchy properties of modern RISC processors. This algorithm is also suited for parallelization on a moderate number of networked workstations.