<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>1361</id>
    <completedYear/>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>habilitation</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-07-27</completedDate>
    <publishedDate>2010-06-20</publishedDate>
    <thesisDateAccepted>2010-06-20</thesisDateAccepted>
    <title language="eng">Mathematical Optimization and Public Transportation</title>
    <abstract language="eng">This cumulative thesis collects the following six papers for obtaining the&#13;
habilitation at the Technische Universität Berlin, Fakultät II – Mathematik&#13;
und Naturwissenschaften:&#13;
(1) Set packing relaxations of some integer programs.&#13;
(2) Combinatorial packing problems.&#13;
(3) Decomposing matrices into blocks.&#13;
(4) A bundle method for integrated multi-depot vehicle and duty scheduling&#13;
in public transit.&#13;
(5) Models for railway track allocation.&#13;
(6) A column-generation approach to line planning in public transport.&#13;
Some changes were made to the papers compared to the published versions.&#13;
These pertain to layout unifications, i.e., common numbering, figure, table,&#13;
and chapter head layout. There were no changes with respect to notation or&#13;
symbols, but some typos have been eliminated, references updated, and some&#13;
links and an index was added. The mathematical content is identical.&#13;
The papers are about the optimization of public transportation systems,&#13;
i.e.,&#13;
bus networks, railways, and airlines, and its mathematical foundations,&#13;
i.e.,&#13;
the theory of packing problems. The papers discuss mathematical models,&#13;
theoretical analyses, algorithmic approaches, and computational aspects of&#13;
and to problems in this area.&#13;
Papers 1, 2, and 3 are theoretical. They aim at establishing a theory of&#13;
packing problems as a general framework that can be used to study traffic&#13;
optimization problems. Indeed, traffic optimization problems can often be&#13;
modelled as path packing, partitioning, or covering problems, which lead&#13;
directly to set packing, partitioning, and covering models. Such models are&#13;
used in papers 4, 5, and 6 to study a variety of problems concerning the&#13;
planning&#13;
of line systems, buses, trains, and crews. The common aim is always&#13;
to exploit as many degrees of freedom as possible, both at the level of the&#13;
individual problems by using large-scale integer programming techniques, as&#13;
well as on a higher level by integrating hitherto separate steps in the&#13;
planning&#13;
process.</abstract>
    <identifier type="urn">urn:nbn:de:0297-zib-13613</identifier>
    <author>Ralf Borndörfer</author>
    <submitter>Ralf Borndörfer</submitter>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>set packing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>set partitioning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>set covering</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>polyhedral combinatorics</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>public transport</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>railways</value>
    </subject>
    <collection role="msc" number="90-02">Research exposition (monographs, survey articles)</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="collections" number="">Habilitationen</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="BMBF-IS">BMBF-IS</collection>
    <collection role="projects" number="LHS-CS">LHS-CS</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="projects" number="Trassenbörse">Trassenbörse</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <thesisPublisher>Zuse Institute Berlin (ZIB)</thesisPublisher>
    <thesisGrantor>Technische Universität Berlin</thesisGrantor>
    <file>https://opus4.kobv.de/opus4-zib/files/1361/Habil_Borndoerfer.pdf</file>
  </doc>
</export-example>
