This paper presents an overview of recovery models and algorithms for real-time railway disturbance and disruption management. This area is currently an active research area in Operations Research, including real-time timetable rescheduling and real-time rescheduling of the rolling stock and crew duties. These topics are addressed in this paper. Also research dealing with the integration of more than one rescheduling phase is discussed. Currently, the developed methods have been tested mainly in an experimental setting, thereby showing promising results, both in terms of their solution quality and in terms of their computation times. The application of these models and algorithms in real-life railway systems will be instrumental for increasing the quality of the provided railway services, leading to an increased utilization of the involved railway systems.
T his paper presents two different models and algorithms for integrated vehicle and crew scheduling in the multiple-depot case. The algorithms are both based on a combination of column generation and Lagrangian relaxation.Furthermore, we compare those integrated approaches with each other and with the traditional sequential one on randomly generated, as well as real-world, data instances for a suburban/extraurban mass transit system. To simulate such a transit system, we propose a new way of randomly generating data instances such that their properties are the same as for our real-world instances. IntroductionVehicle and crew scheduling are two main problems arising in public transport scheduling. Mostly, these problems are considered separately, where first the vehicle-scheduling problem, and afterward the crewscheduling problem, is solved. In this paper we consider the suburban/extraurban transit system with multiple depots, where we investigate the savings of using an integrated approach instead of a sequential one. It is generally expected that the savings of using an integrated approach in a suburban/extraurban transit system are much more significant than in an urban mass transit system because there is much less opportunity to relieve one driver for another one in such a way that both drivers can enjoy their break or start/finish their duty. These reliefs are only allowed at depots and certain other specified locations, which are much further away from each other than in the urban context. If first an optimal vehicle schedule is constructed, there can be vehicles that do not pass a relief location for hours. Therefore, it is very possible that a feasible crew schedule does not exist at all, or, more probably, that the crew schedule will be very inefficient.In this paper we extend the mathematical model and the solution approach that we developed for the single-depot case in Freling, Huisman, and Wagelmans (2003) to the multiple-depot setting. This solution approach is based on Lagrangian relaxation * In Memoriam: Richard Freling passed away on January 29, 2002, at the age of 34.in combination with column generation. The column generation is used to generate a set of duties, while Lagrangian relaxation is used to solve the master problem. Finally, Lagrangian heuristics are used to compute feasible solutions. Furthermore, we formulate another model that is an extension of the model for the single-depot case proposed by Haase, Desaulniers, and Desrosiers (2001), and we show the relation between both models. We also develop an algorithm for this model that is based on the same ideas as the algorithm for the first model. However, an important difference between the single-depot and multiple-depot cases is that in the latter one the underlying vehicle-scheduling problem is NP-hard (see Bertossi, Carraresi, and Gallo 1987), while in the former it can be solved in polynomial time. Of course, the underlying crew-scheduling problem is NP-hard in both cases (see Fischetti, Martello, and Toth 1989).Although a lot of a...
A railway system needs a substantial amount of maintenance. To prevent unexpected breakdowns as much as possible, preventive maintenance is required. In this paper we discuss the Preventive Maintenance Scheduling Problem (PMSP), where (short) routine activities and (long) unique projects have to be scheduled in a certain period. To reduce costs and inconvenience for the travellers and operators, these activities have to be scheduled as much as possible together. We present a mathematical formulation for this problem and some greedy heuristics to solve it fast. Moreover, we compare the performance of these heuristics with the optimal solution using some randomly generated instances.
In this paper we introduce the problem of shunting passenger train units in a railway station. Shunting occurs whenever train units are temporarily not necessary to operate a given timetable. We discuss several aspects of this problem and focus on two subproblems. We propose mathematical models for these subproblems together with a solution method based on column generation. Furthermore, a new efficient and speedy solution technique for pricing problems in column generation algorithms is introduced. Finally, we present computational results based on real life instances from Netherlands Railways.
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