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Institute
This book promotes the use of mathematical optimization and operations research methods in rail transportation. The editors assembled thirteen contributions from leading scholars to present a unified voice, standardize terminology, and assess the state-of-the-art.
There are three main clusters of articles, corresponding to the classical stages of the planning process: strategic, tactical, and operational. These three clusters are further subdivided into five parts which correspond to the main phases of the railway network planning process: network assessment, capacity planning, timetabling, resource planning, and operational planning. Individual chapters cover:
Simulation
Capacity Assessment
Network Design
Train Routing
Robust Timetabling
Event Scheduling
Track Allocation
Blocking
Shunting
Rolling Stock
Crew Scheduling
Dispatching
Delay Propagation
A railway operator creates (rolling stock) rotations in order to have a precise master plan for the
operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply
traverses a set of operational days while covering trips of the timetable. As it is well known,
the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging
and still a topical research subject. Nevertheless, we study a completely different but strongly
related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce
a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In
our industrial application at DB Fernverkehr AG, the handout is exactly as important as the
rotation itself. Moreover, it turns out that also other European railway operators use exactly the
same methodology (but not terminology). Since a rotation can have many handouts of different
quality, we show how to compute optimal ones through an integer program (IP) by standard
software. In addition, a construction as well as an improvement heuristic are presented. Our
computational results show that the heuristics are a very reliable standalone approach to quickly
find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a
computational comparison to the IP approach.
A railway operator creates (rolling stock) rotations in order to have a precise master plan for the operation of a timetable by railway vehicles. A rotation is considered as a cycle that multiply traverses a set of operational days while covering trips of the timetable. As it is well known, the proper creation of rolling stock rotations by, e.g., optimization algorithms is challenging and still a topical research subject. Nevertheless, we study a completely different but strongly related question in this paper, i.e.: How to visualize a rotation? For this purpose, we introduce a basic handout concept, which directly leads to the visualization, i.e., handout of a rotation. In our industrial application at DB Fernverkehr AG, the handout is exactly as important as the rotation itself. Moreover, it turns out that also other European railway operators use exactly the same methodology (but not terminology). Since a rotation can have many handouts of different quality, we show how to compute optimal ones through an integer program (IP) by standard software. In addition, a construction as well as an improvement heuristic are presented. Our computational results show that the heuristics are a very reliable standalone approach to quickly find near-optimal and even optimal handouts. The efficiency of the heuristics is shown via a computational comparison to the IP approach.
Since railway companies have to apply for long-term public contracts to operate railway lines in public tenders, the question how they can estimate the operating cost for long-term periods adequately arises naturally. We consider a rolling stock rotation problem for a time period of ten years, which is based on a real world instance provided by an industry partner. We use a two stage approach for the cost estimation of the required rolling stock. In the first stage, we determine a weekly rotation plan. In the second stage, we roll out this weekly rotation plan for a longer time period and incorporate scheduled maintenance treatments. We present a heuristic approach and a mixed integer programming model to implement the process of the second stage. Finally, we discuss computational results for a real world tendering scenario.
We propose a model for the integrated optimization of vehicle
rotations and vehicle compositions in long distance railway passenger
transport. The main contribution of the paper is a hypergraph model
that is able to handle the challenging technical requirements as
well as very general stipulations with respect to the ``regularity''
of a schedule. The hypergraph model directly generalizes network
flow models, replacing arcs with hyperarcs. Although NP-hard in
general, the model is computationally well-behaved in practice. High
quality solutions can be produced in reasonable time using high
performance Integer Programming techniques, in particular, column
generation and rapid branching. We show that, in this way,
large-scale real world instances of our cooperation partner DB
Fernverkehr can be solved.
For providing railway services the company’s railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride
and it is often related to the image of the company itself. Thus, it is highly desired to
have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see Maroti and Kroon 2005, or Cordeau et. al. 2001 for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer
linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in Borndörfer et. al. 2015. The new approach is tested on real world instances modeling different scenarios
for the ICE high speed train network in Germany and compared to the approaches
of Reuther 2017 that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
For providing railway services the company's railway rolling stock is one if not the most important ingredient. It decides about the number of passenger or cargo trips the company can offer, about the quality a passenger experiences the train ride and it is often related to the image of the company itself. Thus, it is highly desired to have the available rolling stock in the best shape possible. Moreover, in many countries, as Germany where our industrial partner DB Fernverkehr AG (DBF) is located, laws enforce regular vehicle inspections to ensure the safety of the passengers. This leads to rolling stock optimization problems with complex rules for vehicle maintenance. This problem is well studied in the literature for example see [Maróti and Kroon, 2005; Gábor Maróti and Leo G. Kroon, 2007], or [Cordeau et al., 2001] for applications including vehicle maintenance. The contribution of this paper is a new algorithmic approach to solve the Rolling Stock Rotation Problem for the ICE high speed train fleet of DBF with included vehicle maintenance. It is based on a relaxation of a mixed integer linear programming model with an iterative cut generation to enforce the feasibility of a solution of the relaxation in the solution space of the original problem. The resulting mixed integer linear programming model is based on a hypergraph approach presented in [Ralf Borndörfer et al., 2015]. The new approach is tested on real world instances modeling different scenarios for the ICE high speed train network in Germany and compared to the approaches of [Reuther, 2017] that are in operation at DB Fernverkehr AG. The approach shows a significant reduction of the run time to produce solutions with comparable or even better objective function values.
The Cycle Embedding Problem
(2016)
Given two hypergraphs, representing a fine and a coarse "layer", and a cycle cover of the nodes of the coarse layer, the cycle embedding problem (CEP) asks for an embedding of the coarse cycles into the fine layer. The CEP is NP-hard for general hypergraphs, but it can be solved in polynomial time for graphs. We propose an integer rogramming formulation for the CEP that provides a complete escription of the CEP polytope for the graphical case. The CEP comes up in railway vehicle rotation scheduling. We present computational results for problem instances of DB Fernverkehr AG that justify a sequential coarse-first-fine-second planning approach.
We show how to optimize rolling stock rotations that are required for the operation of a passenger timetable. The underlying mathematical ptimization problem is called rolling stock rotation problem (RSRP) and the leitmotiv of the thesis is RotOR, i.e., a highly integrated optimization algorithm for the RSRP. RotOR is used by DB Fernverkehr AG (DBF) in order to optimize intercity express (ICE) rotations for the European high-speed network. In this application, RSRPs have to be solved which (A) require many different aspects to be simultaneously considered, (B) are typically of large scale, and (C) include constraints that have a difficult combinatorial structure. This thesis suggests answers to these issues via the following concepts.
(A) The main model, which RotOR uses, relies on a hypergraph. The hypergraph provides an easy way to model manifold industrial railway requirements in great detail. This includes well known vehicle composition requirements as well as relatively unexplored regularity stipulations. At the same time, the hypergraph directly leads to a mixed-integer programming (MIP) model for the RSRP.
(B) The main algorithmic ingredient to solve industrial instances of the RSRP is a coarse-to-fine (C2F) column generation procedure. In this approach, the hypergraph is layered into coarse and fine layers that distinguish different levels of detail of the RSRP. The coarse layers are algorithmically utilized while pricing fine columns until proven optimality. Initially, the C2F approach is presented in terms of pure linear programming in order to provide an interface for other applications.
(C) Rolling stock rotations have to comply to resource constraints in order to ensure, e.g., enough maintenance inspections along the rotations. These constraints are computationally hard, but are well known in the literature on the vehicle routing problem (VRP). We define an interface problem in order to bridge between the RSRP and the VRP and derive a straightforward algorithmic concept, namely regional search (RS), from their common features and, moreover, differences. Our RS algorithms show promising results for classical VRPs and RSRPs.
In the first part of the thesis we present these concepts, which encompass its main mathematical contribution. The second part explains all modeling and solving components of RotOR that turn out to be essential in its industrial application. The thesis concludes with a solution to a complex re-optimization RSRP that RotOR has computed successfully for DBF. In this application all ICE vehicles of the ICE-W fleets of DBF had to be redirected past a construction site on a high-speed line in the heart of Germany.
Rolling stock optimization is a task that naturally arises by operating a railway system. It could be seen with different level of details. From a strategic perspective to have a rough plan which types of fleets to be bought to a more operational perspective to decide which coaches have to be maintained first. This paper presents a new approach to deal with rolling stock optimisation in case of a (long term) strike. Instead of constructing a completely new timetable for the strike period, we propose a mixed integer programming model that is able to choose appropriate trips from a given timetable to construct efficient tours of railway vehicles covering an optimized subset of trips, in terms of deadhead kilometers and importance of the trips. The decision which trip is preferred over the other is made by a simple evaluation method that is deduced from the network and trip defining data.