Holger Flier

Mining Railway Delay Dependencies in Large-Scale Real-World Delay Data

The propagation of delays between trains has a considerable impact on railway operations. Ideally, planners would like to create timetables that avoid such propagation as much as possible. To improve existing timetables, tools for automatic detection of systematic dependencies of delays among trains would be of great aid. We present efficient algorithms to detect two of the most important types of dependencies, namely dependencies due to resource conflicts and due to maintained connections. We give experimental results on real-world data that demonstrate the practical applicability of our algorithms.

Track Allocation in Freight-Train Classification with Mixed Tracks

We consider the process of forming outbound trains from cars of inbound trains at rail-freight hump yards. Given the arrival and departure times as well as the composition of the trains, we study t ...

Vertex Disjoint Paths for Dispatching in Railways

We study variants of the vertex disjoint paths problem in planar graphs where paths have to be selected from a given set of paths. We study the problem as a decision, maximization, and routing-in-rounds problem. Although all considered variants are NP-hard in planar graphs, restrictions on the location of the terminals, motivated by railway applications, lead to polynomially solvable cases for the decision and maximization versions of the problem, and to a

Scheduling Additional Trains on Dense Corridors

p

Optimal Freight Train Classification using Column Generation

-approximation algorithm for the routing-in-rounds problem, where

Optimization Methods for Multistage Freight Train Formation

p

Maximum independent set in 2-direction outersegment graphs

is the maximum number of alternative paths for a terminal pair.

Combinational Aspects of Move Up Crews

Every train schedule entails a certain risk of delay. When adding a new train to an existing timetable, planners have to take the expected risk of delay of the trains into account. Typically, this can be a very laborious task involving detailed simulations. We propose to predict the risk of a planned train using a series of linear regression models on the basis of extensive real world delay data of trains. We show how to integrate these models into a combinatorial shortest path model to compute a set of Pareto optimal train schedules with respect to risk and travel time. We discuss the consequences of different model choices and notions of risk with respect to the algorithmic complexity of the resulting combinatorial problems. Finally, we demonstrate the quality of our models on real world data of Swiss Federal Railways.

Hump Yard Track Allocation with Temporary Car Storage

We consider planning of freight train classification at hump yards using integer programming. The problem involves the formation of departing freight trains from arriving trains subject to scheduling and capacity constraints. To increase yard capacity, we allow the temporary storage of early freight cars on specific mixed-usage tracks. The problem has previously been modeled using a direct integer programming model, but this approach did not yield lower bounds of sufficient quality to prove optimality. In this paper, we formulate a new extended integer programming model and design a column generation approach based on branch-and-price to solve problem instances of industrial size. We evaluate the method on historical data from the Hallsberg hump yard in Sweden, and compare the results with previous approaches. The new method managed to find optimal solutions in all of the 192 problem instances tried. Furthermore, no instance took more than 13 minutes to solve to optimality using fairly standard computer hardware.

Optimized shunting: with mixed-usage tracks

This paper considers mathematical optimization for the multistage train formation problem, which at the core is the allocation of classification yard formation tracks to outbound freight trains, subject to realistic constraints on train scheduling, arrival and departure timeliness, and track capacity. The problem formulation allows the temporary storage of freight cars on a dedicated mixed-usage track. This real-world practice increases the capacity of the yard, measured in the number of simultaneous trains that can be successfully handled. Two optimization models are proposed and evaluated for the multistage train formation problem. The first one is a column-based integer programming model, which is solved using branch and price. The second model is a simplified reformulation of the first model as an arc-indexed integer linear program, which has the same linear programming relaxation as the first model. Both models are adapted for rolling horizon planning and evaluated on a five-month historical data set from the largest freight yard in Scandinavia. From this data set, 784 instances of different types and lengths, spanning from two to five days, were created. In contrast to earlier approaches, all instances could be solved to optimality using the two models. In the experiments, the arc-indexed model proved optimality on average twice as fast as the column-based model for the independent instances, and three times faster for the rolling horizon instances. For the arc-indexed model, the average solution time for a reasonably sized planning horizon of three days was 16 seconds. Regardless of size, no instance took longer than eight minutes to be solved. The results indicate that optimization approaches are suitable alternatives for scheduling and track allocation at classification yards.