Railway crew capacity planning problem with connectivity of schedules

We study a tactical level crew capacity planning problem in railways which determines the minimum required crew size in a region while both feasibility and connectivity of schedules are maintained. We present alternative mathematical formulations which depend on network representations of the problem. A path-based formulation in the form of a set-covering problem along with a column-and-row generation algorithm is proposed. An arc-based formulation of the problem is solved with a commercial linear programming solver. The computational study illustrates the effect of schedule connectivity on crew capacity decisions and shows that arc-based formulation is a viable approach

A Lagrangian Relaxation Approach Based on a Time-Space-State Network for Railway Crew Scheduling

The crew scheduling problem 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 solve this optimization problem, a solution method is proposed based on a time-space-state network and Lagrangian relaxation. In this method, the "hard constraints" corresponding to the crew rules are described as the state of vertices in the time-space-state network. Based on the network, this problem is modeled as a network flow model, referred to as an initial model. To break the symmetry and improve the strength of the formulation, five valid inequalities are added. To solve the problem, we relax the coupling constraints by Lagrangian relaxation. The resulting subproblems are shortest path problems in the time-space-state networks. We propose a Lagrangian heuristic to find a feasible solution. Finally, the solution method is tested on real-world instances from an intercity rail line and a regional railway network in China. We discuss the effects of additional valid inequalities and the effects of different length of meal time windows

Planejamento da Designação de Maquinistas a Trens de Viagem de Longa Distância em Ferrovias de Carga

Nas ferrovias, trens circulam para transportar cargas e cada trem é conduzido por um maquinista. As ferrovias de cargas possuem grandes extensões e, o tempo de viagem dos trens da origem ao destino é, geralmente, superior à escala de trabalho dos maquinistas, sendo necessário realizar a troca destes maquinistas durante a viagem. As ferrovias são divididas em trechos onde existe um destacamento, onde os maquinistas se apresentam para conduzir os trens e onde ocorre a troca de maquinista. Este artigo apresenta um modelo matemático para elaboração da designação de maquinistas para atender os trens que passarão pelo destacamento, buscando minimizar o pagamento de horas extras e atendendo as determinações legais. O modelo propõe uma abordagem diferenciada para descrever matematicamente o problema, algo que ainda não foi encontrado na literatura. Os resultados demonstram a efetividade no planejamento das designações dos maquinistas, podendo proporcionar economia com o pagamento de horas extras

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

Modeling and Solving of Railway Optimization Problems

The main aim of this work is to provide decision makers suitable approaches for solving two crucial planning problems in the railway industry: the locomotive assignment problem and the crew scheduling problem with attendance rates. On the one hand, the focus is on practical usability and the necessary integration and consideration of real-life requirements in the planning process. On the other hand, solution approaches are to be developed, which can provide solutions of sufficiently good quality within a reasonable time by taking all these requirements into account