Single-Car Routing in Rail Freight Transport

Abstract

Single cars in rail freight service are bundled into trains at classification yards. On the way from their respective origins via intermediate yards to their destinations, they are reclassified several times, which is a time-consuming and personally consuming procedure. The single-car routing problem asks for the design of such routes for a given set of orders (origin-destination pairs with associated data) on an infrastructure network, such that the number of trains and their travel distances are minimal. A number of hard restrictions must be obeyed, such as restrictions for the train length and weight, and capacity restrictions for the yards, as well as further operational rules. We present a mixed-integer linear programming (MILP) formulation for this car-routing problem arising at Deutsche Bahn, one of the largest European railway companies. In a further step, we refine the handling of the turnover waiting time for the cars in the yards, which leads to the inclusion of nonlinear constraints in the model. Using adequate linearization techniques, this model can be reduced to a MILP again. Instances of this model turn out to be hard to solve. Further techniques are thus presented to speed up the numerical solution process, among them a tree-based reformulation and heuristic cuts. The different model formulations are computationally compared on a test set of randomly generated instances whose sizes are comparable to real-world instances. Using state-of-the-art MILP solvers, optimal or near-optimal solutions can be computed within a reasonable time frame.

One-block train formation in large-scale railway networks: An exact model and a tree-based decomposition algorithm

“…Jin et al To the best knowledge of the authors, almost none of the current contributions integrates the intree rule into the train formation problem. Among the few that do, Bodin et al (1980), Jarrah et al (2009) and Fugenschuh et al (2015)…”

“…However, such an assumption may not cover applications in transportation systems where the unitary rule holds, for example, express package delivery (Barnhart et al 2002) or hazardous material transportation (Verter and Kara 2008). The intree rule is only applied by Bodin et al (1980), Lin et al (2012) and Fugenschuh et al (2015) in railways, and by Jarrah et al (2009) in less-than-truckload transportation, where it is called a pure strategy constraint, a reclassification strategy, a unique successor rule or a load-planning requirement, respectively. There has been limited success applying models based on North American or European rail networks to the Chinese context.…”

A comparison of North American and European railway systems

“…The property 'split table' is marked if the model allows to split the wagonflow of particular relations and send its wagons along more than one path to its destination. The so called consolidation effect, which was already described by Assad [2], Fuegenschuh [9] and Voll [14] is denoted in the second row. It will turn out to be a key aspect in our comparison of North American and European models.…”

“…The abolition of the aforementioned pure strategy included in Bodin [4], Keaton [10] and Fuegenschuh [9] might be a key to make European railroad systems more flexible and more efficient. Pure strategy is often used because of historical reasons.…”

An Optimization Method for the Train Service Network Design Problem

“…However, they only considered single-block trains. Fügenschuh et al [13] presented a linear mixed-integer model for the car routing problem arising from Deutsche Bahn's operations. e model sought the most economical car routing, and considered train and car travel kilometers and the amount of used sorting tracks.…”