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  <doc>
    <id>2850</id>
    <completedYear>2000</completedYear>
    <publishedYear>2000</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>45</pageFirst>
    <pageLast>76</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>incollection</type>
    <publisherName>Vieweg Verlag</publisherName>
    <publisherPlace>Braunschweig/Wiesbaden</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Der schnellste Weg zum Ziel</title>
    <parentTitle language="eng">Alles Mathematik</parentTitle>
    <identifier type="doi">10.1007/978-3-322-96366-6_5</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-4209</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Martin Aigner</editor>
    <author>Martin Grötschel</author>
    <editor>Ehrhard Behrends</editor>
    <author>Andreas Löbel</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
  </doc>
  <doc>
    <id>219</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1996-03-04</completedDate>
    <publishedDate>1996-03-04</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr</title>
    <abstract language="eng">This paper addresses the problem of scheduling vehicles in a public mass transportation system. We show how this problem can be modelled as a special multicommodity flow problem and outline the solution methodology we have developed. Based on polyhedral investigations, we have designed and implemented a branch&amp;cut algorithm and various heuristics with which real vehicle scheduling problems of truely large scale can be solved to optimality. We describe some implementation issues and report computational results.</abstract>
    <identifier type="serial">SC-96-08</identifier>
    <identifier type="opus3-id">219</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-2195</identifier>
    <enrichment key="SourceTitle">Erschienen in: Mathematik : Schlüsseltechnologie für die Zukunft; Verbundprojekte zwischen Universität und Industrie. K.-H. Hoffmann u.a. (Hrsg.) Berlin u.a.: Springer 1997. S. 609-624</enrichment>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <author>Manfred Völker</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-96-08</number>
    </series>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/219/SC-96-08.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/219/SC-96-08.pdf</file>
  </doc>
  <doc>
    <id>352</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-03-11</completedDate>
    <publishedDate>1998-03-11</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimization of Transportation Systems</title>
    <abstract language="eng">The world has experienced two hundred years of unprecedented advances in vehicle technology, transport system development, and traffic network extension. Technical progress continues but seems to have reached some limits. Congestion, pollution, and increasing costs have created, in some parts of the world, a climate of hostility against transportation technology. Mobility, however, is still increasing. What can be done? There is no panacea. Interdisciplinary cooperation is necessary, and we are going to argue in this paper that {\em Mathematics\/} can contribute significantly to the solution of some of the problems. We propose to employ methods developed in the {\em Theory of Optimization\/} to make better use of resources and existing technology. One way of optimization is better planning. We will point out that {\em Discrete Mathematics\/} provides a suitable framework for planning decisions within transportation systems. The mathematical approach leads to a better understanding of problems. Precise and quantitative models, and advanced mathematical tools allow for provable and reproducible conclusions. Modern computing equipment is suited to put such methods into practice. At present, mathematical methods contribute, in particular, to the solution of various problems of {\em operational planning}. We report about encouraging {\em results\/} achieved so far.</abstract>
    <identifier type="serial">SC-98-09</identifier>
    <identifier type="opus3-id">353</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3529</identifier>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-09</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Transportation Systems</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Optimization</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Discrete Mathematics</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="BMBF-VS">BMBF-VS</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/352/SC-98-09.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/352/SC-98-09.pdf</file>
  </doc>
  <doc>
    <id>3113</id>
    <completedYear>1997</completedYear>
    <publishedYear>1997</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>609</pageFirst>
    <pageLast>624</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimierung des Fahrzeugumlaufs im Öffentlichen Nahverkehr</title>
    <parentTitle language="eng">Mathematik</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-2195</enrichment>
    <author>Martin Grötschel</author>
    <editor>Karl-Heinz Hoffmann</editor>
    <author>Andreas Löbel</author>
    <editor>Willi Jäger</editor>
    <author>Manfred Völker</author>
    <editor>Thomas Lohmann</editor>
    <editor>Hermann Schunck (Hrsg.)</editor>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-VS">BMBF-VS</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>628</id>
    <completedYear/>
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    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
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    <type>reportzib</type>
    <publisherName/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2001-01-31</completedDate>
    <publishedDate>2001-01-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Duty Scheduling in Public Transit</title>
    <abstract language="eng">This article is about \emph{adaptive column generation techniques} for the solution of duty scheduling problems in public transit. The current optimization status is exploited in an adaptive approach to guide the subroutines for duty generation, LP resolution, and schedule construction toward relevant parts of a large problem. Computational results for three European scenarios are reported.</abstract>
    <identifier type="serial">01-02</identifier>
    <identifier type="opus3-id">629</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6286</identifier>
    <identifier type="doi">10.1007/978-3-642-55753-8_50</identifier>
    <enrichment key="SourceTitle">Appeared in: Mathematics - Key Technology for the Future. W. Jäger, H.-J. Krebs (eds.) Springer 2003, pp. 653-674</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <series>
      <title>ZIB-Report</title>
      <number>01-02</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Duty Scheduling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Constraint Shortest Paths Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Column Generation</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90B06">Transportation, logistics</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="institutes" number="">ZIB Allgemein</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/628/ZR-01-02.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/628/ZR-01-02.pdf</file>
  </doc>
  <doc>
    <id>3158</id>
    <completedYear>2003</completedYear>
    <publishedYear>2003</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>653</pageFirst>
    <pageLast>674</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>incollection</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Duty Scheduling in Public Transit</title>
    <parentTitle language="eng">MATHEMATICS – Key Technology for the Future</parentTitle>
    <identifier type="doi">10.1007/978-3-642-55753-8_50</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-6286</enrichment>
    <author>Martin Grötschel</author>
    <editor>Willi Jäger</editor>
    <author>Ralf Borndörfer</author>
    <editor>Hans-Joachim Krebs</editor>
    <author>Andreas Löbel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="PTVIS">PTVIS</collection>
    <collection role="projects" number="ZIB-Multicore">ZIB-Multicore</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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  <doc>
    <id>3119</id>
    <completedYear>1998</completedYear>
    <publishedYear>1998</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>379</pageFirst>
    <pageLast>409</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>2</volume>
    <type>bookpart</type>
    <publisherName>Brepols Publisher</publisherName>
    <publisherPlace>Turnhout</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Alcuin’s Transportation Problems and Integer Programming</title>
    <parentTitle language="eng">Charlemagne and his Heritage. 1200 Years of Civilization and Science in Europe. Karl der Grosse und sein Nachwirken . 1200 Jahre Kultur und Wissenschaft in Europa</parentTitle>
    <enrichment key="Series">Mathematical Arts</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-1932</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Paul Leo Butzer</editor>
    <author>Martin Grötschel</author>
    <editor>Hubertus Jongen</editor>
    <author>Andreas Löbel</author>
    <editor>Walter Oberschelp</editor>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="BMBF-VS">BMBF-VS</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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    <id>3197</id>
    <completedYear>2010</completedYear>
    <publishedYear>2010</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>27</pageFirst>
    <pageLast>51</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName>American Mathematical Society</publisherName>
    <publisherPlace>Providence, Rhode Iland, USA</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Quickest Path to the Goal</title>
    <parentTitle language="eng">Mathematics Everywhere</parentTitle>
    <identifier type="url">http://www.ams.org/bookstore-getitem/item=MBK-72</identifier>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-11840</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Martin Aigner</editor>
    <author>Martin Grötschel</author>
    <editor>Ehrhard Behrends</editor>
    <author>Andreas Löbel</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>420</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1999-09-17</completedDate>
    <publishedDate>1999-09-17</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Der Schnellste Weg zum Ziel</title>
    <abstract language="deu">Wir geben eine Einführung in die Mathematik von und mit Wegen. Nicht auf dem kürzesten, aber auf einem hoffentlich kurzweiligen Weg!</abstract>
    <identifier type="serial">SC-99-32</identifier>
    <identifier type="opus3-id">421</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-4209</identifier>
    <identifier type="doi">10.1007/978-3-322-96366-6_5</identifier>
    <enrichment key="SourceTitle">Appeared in: Aigner u. Behrends (Eds.) (2000), Alles Mathematik, Vieweg Verlag. S. 45-76</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-99-32</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Kürzeste Wege</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Kombinatorische Optimierung</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Operations Research</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</collection>
    <collection role="msc" number="90C10">Integer programming</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="projects" number="BMBF-DS">BMBF-DS</collection>
    <collection role="projects" number="MATHEON-B1">MATHEON-B1</collection>
    <collection role="projects" number="SenWiFo-Telebus">SenWiFo-Telebus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/420/SC-99-32.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/420/SC-99-32.pdf</file>
  </doc>
  <doc>
    <id>2891</id>
    <completedYear>2001</completedYear>
    <publishedYear>2001</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Integrierte Umlauf- und Dienstplanung im öffentlichen Nahverkehr</title>
    <parentTitle language="eng">Neue Mathematische Verfahren in Industrie und Dienstleistungen</parentTitle>
    <enrichment key="Series">BMBF Mathematikprogramm 03GRM2B4</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-6773</enrichment>
    <author>Ralf Borndörfer</author>
    <author>Martin Grötschel</author>
    <author>Andreas Löbel</author>
    <author>Steffen Weider</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="groetschel">Grötschel, Martin</collection>
    <collection role="persons" number="loebel">Löbel, Andreas</collection>
    <collection role="persons" number="weider">Weider, Steffen</collection>
    <collection role="projects" number="BMBF-IS">BMBF-IS</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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