Integrating Timetabling and Crew

We investigate to what degree we can integrate a Train Timetabling / Engine Scheduling Problem with a Crew Scheduling Problem. In the Timetabling Problem we design a timetable for the desired lines by fixing the departure and arrival times. Also, we allocate time-slots in the network to secure a feasible timetable. Next, we assign engines in the Engine Scheduling Problem to the lines in accordance with the timetable. The overall integration is achieved by obtaining an optimal solution for the Timetabling / Engine Scheduling Problem. We exploit the fact that numerous optimal, and near optimal solutions exists. We consider all solutions that can be obtained from the optimal engine schedule by altering the timetable, while keeping the order of demands in the schedules intact. The Crew Scheduling model is allowed to re-time the service of demands if the additional cost is outweighed by the crew savings. This information is implemented in a mathematical model for the Crew Scheduling Problem. The model is solved using a column generation scheme. Hereby it is possible for the Crew Scheduling algorithm to adjust the timetable and achieve a better overall solution. We perform computational experiments based on a case at a freight railway operator, DB Schenker Rail Scandinavia, and show that significant cost savings can be achieved

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

Evolutionary algorithms for scheduling operations

While business process automation is proliferating through industries and processes, operations such as job and crew scheduling are still performed manually in the majority of workplaces. The linear programming techniques are not capable of automated production of a job or crew schedule within a reasonable computation time due to the massive sizes of real-life scheduling problems. For this reason, AI solutions are becoming increasingly popular, specifically Evolutionary Algorithms (EAs). However, there are three key limitations of previous studies researching application of EAs for the solution of the scheduling problems. First of all, there is no justification for the selection of a particular genetic operator and conclusion about their effectiveness. Secondly, the practical efficiency of such algorithms is unknown due to the lack of comparison with manually produced schedules. Finally, the implications of real-life implementation of the algorithm are rarely considered. This research aims at addressing all three limitations. Collaborations with DBSchenker,the rail freight carrier, and Garnett-Dickinson, the printing company,have been established. Multi-disciplinary research methods including document analysis, focus group evaluations, and interviews with managers from different levels have been carried out. A standard EA has been enhanced with developed within research intelligent operators to efficiently solve the problems. Assessment of the developed algorithm in the context of real life crew scheduling problem showed that the automated schedule outperformed the manual one by 3.7% in terms of its operating efficiency. In addition, the automatically produced schedule required less staff to complete all the jobs and might provide an additional revenue opportunity of £500 000. The research has also revealed a positive attitude expressed by the operational and IT managers towards the developed system. Investment analysis demonstrated a 41% return rate on investment in the automated scheduling system, while the strategic analysis suggests that this system can enable attainment of strategic priorities. The end users of the system, on the other hand, expressed some degree of scepticism and would prefer manual methods

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

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 Generalized Network Model for Freight Car Distribution

We consider the empty freight car distribution problem (DP) at DB Schenker Rail Deutschland AG under a wide range of application relevant constraints and real data sets. The (DP) is an online assignment problem between geographically distributed empty freight car supplies and customer demands for such cars in preparation of good transport. The objective is to minimize transport costs for empty cars while distributing them effectively with respect to the constraints. In our case, one major constraint is given by prescheduled freight trains: obviously a supply can only be assigned to a demand if it reaches the latter in time. Further, the variety of goods (bulk cargo, steel coils, etc.) to be transported requires distinct types of freight cars. Freight cars of a certain type can be exchanged by cars of other types with respect to a given substitution scheme and different 'exchange rates'. Allowed substitutions are therefore another major constraint of the (DP). We describe further `hard' and `soft' constraints and sketch the current work flow at DB Schenker Rail Deutschland AG to find an adequate solution for the (DP) on a daily base in practice. The (DP) is currently solved separately for groups of car types and in several steps. Moreover, some steps contain manual pre- and post-processing to ensure certain constraints. Hence global sub-optimal distributions can occur. We therefore integrate all constraints into a generalized network flow model for the (DP). A global optimal distribution is then provided by an integral minimum cost flow in the network. To find such a flow is NP-hard in general. We show that a general substitution scheme makes our notion of the (DP) also NP-hard. Hence independent of the applied model and with respect to practical runtime requirements, we have to find a compromise between solution time and quality. We do so in two ways. Instances of the (DP) which correspond to classical flow networks are solved by an integral minimum cost flow, which can be obtained in polynomial time. We use such instances to polynomially obtain minimum cost flows of fixed bounded fractionality for certain general instances. For those instances occurring in the application we obtain half-integral flows, which can be rounded to approximate or heuristic distributions in linear time. Moreover, we develop a network-based reoptimization approach, which yields optimal solutions for subsequent instances with few changes very fast. This thesis was inspired and funded by a 2-year research and development project of DB Schenker Rail Deutschland AG in cooperation with the work group Faigle/Schrader of the University of Cologne and the work group of Prof. Dr. Sven O. Krumke at the Technical University of Kaiserslautern. The project included the implementation of the generalized network model and the reoptimization, approximation and heuristic methods. The software is designed as a future optimization kernel for the (DP) at DB Schenker Rail Deutschland AG

Crew Management in Passenger Rail Transport

__Abstract__ Crew management in passenger rail transport is an important factor that contributes to both the quality of service to the railway passengers and to the operational costs of the train operating company. This thesis describes how the (railway) Crew Management process can be improved with the introduction of advanced decision support systems, based on advanced mathematical models and algorithms. We provide a managerial perspective on the change process, related to the introduction of these systems, and give an overview of the lessons learned. We have shown that introducing decision support can give substantial improvements in the overall performance of a railway company. Within NS, the support for the Crew Management process has led to a stable relationship between management and train crew. In addition, the lead-time of the planning process is shortened from months to hours and NS is now able to perform scenario analyses, e.g., to study effects of adjusting the labour rules. Also, NS can adjust their service when severe weather conditions are expected, by creating a specific winter timetable shortly before the day of operation. Finally, we also introduced a decision support system for real-time rescheduling of crew duties on the day of operations. This enables us to adapt the actual crew schedules very quickly. As a result, we reduce the number of cancelled trains and fewer trains will be delayed in case of unforeseen disruptions