Railway Track Allocation – Models and Algorithms

244 Pages·2012·4.27 MB·English

by  Thomas Schlechte

Railway Track Allocation: Models and
Algorithms
vorgelegt von
Dipl.-Math. oec. Thomas Schlechte
aus Halle an der Saale
Von der Fakult¨at II – Mathematik und Naturwissenschaften
der Technischen Universit¨at Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte Dissertation
Promotionsausschuss
Berichter: Prof.Dr.Dr.h.c.mult.MartinGr¨otschel
PD Dr. habil. Ralf Bornd¨orfer
Vorsitzender: Prof. Dr. Fredi Tro¨ltzsch
Tag der wissenschaftlichen Aussprache: 23.12.2011
Berlin 2012
D 83

Railway Track Allocation: Models
and Algorithms
Thomas Schlechte

Preface
The “heart” of a railway system is the timetable. Each railway opera-
tor has to decide on the timetable to offer and on the rolling stock to
operate the trips of the trains. For the railway infrastructure manager
the picture is slightly different – trains have to be allocated to rail-
way tracks and times, called slots such that all passenger and freight
transport operators are satisfied and all train movements can be car-
ried out safely. This problem is called the track allocation problem. My
thesis deals with integer programming models and algorithmic solution
methods for the track allocation problem in real world railway systems.
My work on this topic has been initiated and motivated by the in-
terdisciplinary research project “railway slot allocation” or in German
“Trassenb¨orse”.1 Thisprojectinvestigatedthequestionwhetheracom-
petitive marketing of a railway infrastructure can be achieved using an
auction-based allocation of railway slots. The idea is that competing
train operating companies (TOCs) can bid for any imaginable use of
the infrastructure. Possible conflicts will be resolved in favor of the
party with the higher willingness to pay, which leads directly to the
question of finding revenue maximal track allocations. Moreover a
fair and transparent mechanism “cries” out for exact optimization ap-
proaches, because otherwise the resulting allocation is hardly accept-
able and applicable in practice. This leads to challenging questions
in economics, railway engineering, and mathematical optimization. In
particular, developing models that build a bridge between the abstract
world of mathematics and the technical world of railway operations
was an exciting task.
I worked on the “Trassenbo¨rse” project with partners from different ar-
eas, namely, on economic problems with the Workgroup for Economic
and Infrastructure Policy (WIP) at the Technical University of Berlin
(TU Berlin), on railway aspects with the Chair of Track and Rail-
way Operations (SFWBB) at TU Berlin, the Institute of Transport,
Railway Construction and Operation (IVE) at the Leibniz Universita¨t
Hannover, and the Management Consultants Ilgmann Miethner Part-
ner (IMP).
1This project was funded by the Federal Ministry of Education and Research
(BMBF),Grantnumber19M2019andtheFederalMinistryofEconomicsandTech-
nology (BMWi), Grant number 19M4031A and Grant number 19M7015B.
This thesis is written from the common perspective of all persons I
worked closely with, especially the project heads Ralf Borndo¨rfer and
Martin Gr¨otschel, project partners Gottfried Ilgmann and Klemens
Polatschek, and the ZIB colleagues Berkan Erol, Elmar Swarat, and
Steffen Weider.
The highlight of the project was a cooperation with the Schweizerische
Bundesbahnen (SBB) on optimizing the cargo traffic through the Sim-
plontunnel, oneofthemajortransitroutesintheAlps. Thisrealworld
application was challenging in many ways. It provides the opportunity
to verify the usefulness of our methods and algorithms by computing
high quality solutions in a fully automatic way.
The material covered in this thesis has been presented at several in-
ternational conferences, e.g., European Conference on Operational Re-
search (EURO 2009, 2010), Conference on Transportation Scheduling
and Disruption Handling, Workshop on Algorithmic Approaches for
Transportation Modeling, Optimization, and System (ATMOS 2007,
2010), International Seminar on Railway Operations Modeling and
Analysis (ISROR 2007, 2009, 2011), Symposium on Operations Re-
search (OR 2005, 2006, 2007, 2008), International Conference on Com-
puter System Design and Operation in the Railway and other Transit
Systems (COMPRAIL), International Conference on Multiple Criteria
Decision Making (MCDM), World Conference on Transport Research
(WCTR). Significant parts have already been published in various ref-
ereed conference proceedings and journals:
(cid:46) Borndo¨rfer et al. (2006) [34],
(cid:46) Borndo¨rfer et al. (2005) [33],
(cid:46) Borndo¨rfer & Schlechte (2007) [31],
(cid:46) Borndo¨rfer & Schlechte (2007) [30],
(cid:46) Erol et al. (2008) [85],
(cid:46) Schlechte & Borndo¨rfer (2008) [188],
(cid:46) Borndo¨rfer, Mura & Schlechte (2009) [40],
(cid:46) Borndo¨rfer, Erol & Schlechte (2009) [38],
(cid:46) Schlechte & Tanner (2010) [189]3,
(cid:46) Borndo¨rfer, Schlechte & Weider (2010) [43],
(cid:46) Schlechte et al. (2011) [190],1
(cid:46) and Bornd¨orfer et al. (2010) [42]2.
1accepted by Journal of Rail Transport Planning & Management.
2accepted by Annals of Operations Research.
3submitted to Research in Transportation Economics.
Research Goals and Contributions
The goal of the thesis is to solve real world track allocation problems
by exact integer programming methods. In order to establish a fair and
transparent railway slot allocation, exact optimization approaches are
required, as well as accurate and reliable railway models. Integer pro-
gramming based methods can provide excellent guarantees in practice.
We successfully identified and tackled several tasks to achieve these
ambitious goals:
1. applying a novel modeling approach to the track allocation prob-
lem called “configuration” models and providing a mathematical
analysis of the associated polyhedron,
2. developing a sophisticated integer programming approach called
“rapidbranching”thathighlyutilizesthecolumngenerationtech-
niqueandthebundlemethodtotacklelargescaletrackallocation
instances,
3. developing a Micro-Macro Transformation, i.e., a bottom-up ag-
gregation, approach to railway models of different scale to pro-
duce a reliable macroscopic problem formulation of the track al-
location problem,
4. providingastudycomparingtheproposedmethodologytoformer
approaches, and,
5. carrying out a comprehensive real world data study for the Sim-
plon corridor in Switzerland of the “entire” optimal railway track
allocation framework.
In addition, we present extensions to incorporate aspects of robustness
and we provide an integration and empirical analysis of railway slot
allocation in an auction based framework.
Thesis Structure
A rough outline of the thesis is shown in Figure 1. It follows the
“solution cycle of applied mathematics”. In a first step the real world
problem is analyzed, then the track allocation problem is translated
into a suitable mathematical model, then a method to solve the models
in an efficient way is developed, followed by applying the developed
methodology in practice to evaluate its performance. Finally, the loop
is closed by re-translating the results back to the real world application
and analyze them together with experts and practitioners.
Main concepts on planning problems in railway transportation are pre-
sented in Chapter I. Railway modeling and infrastructure capacity is
the main topic of Chapter II. Chapter III focuses on the mathematical
modeling and the solution of the track allocation problem. Finally,
Chapter IV presents results for real world data as well as for ambitious
hypothetical auctioning instances.
1 Introduction
2 Planning Process
Chapter I 3 Network Design
- 4 Freight Service Network Design
Planning in Railway 5 Line Planning
Transportation 6 Timetabling
7 Rolling Stock Planning
8 Crew Scheduling
Chapter II 1 Microscopic Railway Modeling
- 2 Macroscopic Railway Modeling
Railway Modeling 3 Final Remarks and Outlook
Chapter III
1 The Track Allocation Problem
-
2 Integer Programming Models
Railway Track
3 Branch and Price
Allocation
1 Model Comparison
Chapter IV
2 Algorithmic Ingredients
-
3 Auction Experiments
Case Studies
4 The Simplon Corridor
Figure 1: Structure of the thesis.