Railway transportation systems are important for society and have many challenging and important planning problems. Train services as well as maintenance of a railway network need to be scheduled efficiently, but have mostly been treated as two separate planning problems. Since these activities are mutually exclusive they must be coordinated and should ideally be planned together. In this paper we present a mixed integer programming model for solving an integrated railway traffic and network maintenance problem. The aim is to find a long term tactical plan that optimally schedules train free windows sufficient for a given volume of regular maintenance together with the wanted train traffic. A spatial and temporal aggregation is used for controlling the available network capacity. The properties of the proposed model are analysed and computational experiments on various synthetic problem instances are reported. Model extensions and possible modifications are discussed as well as future research directions.

I n this paper, we consider empty freight car distribution in a scheduled railway system. We analyze the cost structure for the repositioning of empty cars, and conclude that the distribution cost shows an economyof-scale behavior. In addition to the cost proportional to the number of cars sent from origin to destination, there is a cost related to car-handling operations at yards, which depends on the number of car groups that are handled. Thus, if we can find a transportation pattern in which fewer but larger groups of cars are built, the total distribution cost can be decreased. The objective of the paper is to propose an optimization model that explicitly takes this economy-of-scale effect into account. We use a time-dependent network to describe the possible car movements in time and space, and show how this network can be transformed into a network with fixed costs on links representing movements of cars with identical origin and destination terminals. The resulting optimization model is a capacitated network design model, where each capacity constraint limits the flow on several arcs. We describe a tabu heuristic for solving the model, and present computational results.

In this paper we consider the problem of distributing empty freight cars in a railway company. We describe and analyze the current planning process, identify the shortcomings of the process, and stress the importance of a reliable distribution process for satisfying customer demand and reducing capital costs. We show how the process can be improved using an optimization model which includes capacity constraints on the trains and adheres explicitly to the arrival and departure times of the trains. The optimization model can be characterized as a multicommodity network flow model with integer requirements. Computational tests show that the model can be solved in acceptable time for real size problems, and indicate that the model generates distribution plans that can improve the quality of the planning process.

The Swedish Transport Administration is introducing a new regime, called maintenance windows, for allocating train free slots reserved for maintenance tasks on the railway infrastructure. In this paper, a model for the assessment and the dimensioning of such maintenance windows is presented, which considers marginal effects on both the maintenance cost and the expected train traffic demand. The aim is to establish quantitative measures that can be used for comparing conflicting capacity requests from infrastructure maintenance and traffic operations on railway networks. The model is demonstrated in a cost benefit analysis for a real life case study on the Swedish Northern Main Line.

This paper considers multi-stage train formation with mixed usage tracks at a marshalling yard without departure yard. A novel integer programming model for scheduling shunting tasks as well as allocating arrival yard tracks and classification bowl tracks is presented. By taking a comprehensive view of the marshalling yard operations, more effective schedules can be found, and a variety of characteristics can be optimised, including shunting work effort, number or cost of tracks, and shunting task start times. Two different objective functions are evaluated: minimising work effort in terms of wagon pull-backs and minimising track costs. A procedure for finding a hot-start solution with few wagon pull-backs is also presented. The proposed model is tested on real data from Sävenäs marshalling yard in Sweden. The results show that the method is able to return an optimal schedule for a planning period of 4 days if the hot-start solution is optimal or the remaining problem is tractable for the heuristics in CPLEX.

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