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  <doc>
    <id>2868</id>
    <completedYear>2008</completedYear>
    <publishedYear>2008</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>449</pageFirst>
    <pageLast>454</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>SPRINGER</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">When Periodic Timetables are Suboptimal</title>
    <parentTitle language="eng">Operations Research Proceedings 2007</parentTitle>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-9151</enrichment>
    <author>Ralf Borndörfer</author>
    <editor>Jörg Kalcsics</editor>
    <author>Christian Liebchen</author>
    <editor>Stefan Nickel</editor>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6436</id>
    <completedYear/>
    <publishedYear>2017</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">A Propagation Approach to Acyclic Rolling Stock Rotation Optimization</title>
    <abstract language="eng">The rolling stock, i.e., railway vehicles, are one of the key ingredients of a running railway system. As it is well known, the offer of a railway company to their customers, i.e., the railway timetable, changes from time to time. Typical reasons for that are different timetables associated with different seasons, maintenance periods or holidays. Therefore, the regular lifetime of a timetable is split into (more or less) irregular periods where parts of the timetable are changed. In order to operate a railway timetable most railway companies set up sequences that define the operation of timetabled trips by a single physical railway vehicle called (rolling stock) rotations. Not surprisingly, the individual parts of a timetable also affect the rotations. More precisely, each of the parts brings up an acyclic rolling stock rotation problem with start and end conditions associated with the beginning and ending of the corresponding period. In this paper, we propose a propagation approach to deal with large planning horizons that are composed of many timetables with shorter individual lifetimes. The approach is based on an integer linear programming formulation that propagates rolling stock rotations through the irregular parts of the timetable while taking a large variety of operational requirements into account. This approach is implemented within the rolling stock rotation optimization framework ROTOR used by DB Fernverkehr AG, one of the leading railway operators in Europe. Computational results for real world scenarios are presented to evaluate the approach.</abstract>
    <parentTitle language="eng">Proceedings of the IAROR conference RailLille</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-63930</enrichment>
    <author>Boris Grimm</author>
    <submitter>Boris Grimm</submitter>
    <author>Ralf Borndörfer</author>
    <author>Markus Reuther</author>
    <author>Stanley Schade</author>
    <author>Thomas Schlechte</author>
    <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="grimm">Grimm, Boris</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="persons" number="schade">Schade, Stanley</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>4787</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>10</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>22</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Case Study on Optimizing Toll Enforcements on Motorways</title>
    <abstract language="eng">In this paper we present the problem of computing optimal tours of toll inspectors on German motorways. This problem is a special type of vehicle routing problem and builds up an integrated model, consisting of a tour planning and a duty rostering part. The tours should guarantee a network-wide control whose intensity is proportional to given spatial and time dependent traffic distributions. We model this using a space-time network and formulate the associated optimization problem by an integer program (IP). Since sequential approaches fail, we integrated the assignment of crews to the tours in our model. In this process all duties of a crew member must fit in a feasible roster. It is modeled as a Multi-Commodity Flow Problem in a directed acyclic graph, where specific paths correspond to feasible rosters for one month. We present computational results in a case-study on a German subnetwork which documents the practicability of our approach.</abstract>
    <parentTitle language="eng">3rd Student Conference on Operational Research</parentTitle>
    <identifier type="doi">10.4230/OASIcs.SCOR.2012.1</identifier>
    <enrichment key="Series">OpenAccess Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-15498</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Elmar Swarat</submitter>
    <author>Guillaume Sagnol</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5827</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted>2017</thesisYearAccepted>
    <language>eng</language>
    <pageFirst>383</pageFirst>
    <pageLast>406</pageLast>
    <pageNumber>24</pageNumber>
    <edition>252</edition>
    <issue/>
    <volume>252(2)</volume>
    <type>article</type>
    <publisherName>Springer US</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2016-03-10</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>2017-05-01</thesisDateAccepted>
    <title language="eng">Optimal duty rostering for toll enforcement inspectors</title>
    <abstract language="eng">We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.</abstract>
    <parentTitle language="eng">Annals of Operations Research</parentTitle>
    <identifier type="doi">10.1007/s10479-016-2152-1</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-45107</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Elmar Swarat</submitter>
    <author>Guillaume Sagnol</author>
    <author>Thomas Schlechte</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6027</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber>15</pageNumber>
    <edition/>
    <issue/>
    <volume>54</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving Time Dependent Shortest Path Problems on Airway Networks Using Super-Optimal Wind</title>
    <abstract language="eng">We study the Flight Planning Problem for a single aircraft, which deals with finding a path of minimal travel time in an airway network. Flight time along arcs is affected by wind speed and direction, which are functions of time. We consider three variants of the problem, which can be modeled as, respectively, a classical shortest path problem in a metric space, a time-dependent shortest path problem with piecewise linear travel time functions, and a time-dependent shortest path problem with piecewise differentiable travel time functions. The shortest path problem and its time-dependent variant have been extensively studied, in particular, for road networks. Airway networks, however, have different characteristics: the average node degree is higher and shortest paths usually have only few arcs. We propose A* algorithms for each of the problem variants. In particular, for the third problem, we introduce an application-specific "super-optimal wind" potential function that overestimates optimal wind conditions on each arc, and establish a linear error bound. We compare the performance of our methods with the standard Dijkstra algorithm and the Contraction Hierarchies (CHs) algorithm. Our computational results on real world instances show that CHs do not perform as well as on road networks. On the other hand, A* guided by our potentials yields very good results. In particular, for the case of piecewise linear travel time functions, we achieve query times about 15 times shorter than CHs.</abstract>
    <parentTitle language="eng">16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2016.12</identifier>
    <enrichment key="Series">OpenAccess Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <submitter>Nam-Dung Hoang</submitter>
    <author>Marco Blanco</author>
    <editor>Goerigk Marc</editor>
    <translator>Werneck Renato</translator>
    <author>Ralf Borndörfer</author>
    <author>Nam-Dung Hoang</author>
    <author>Anton Kaier</author>
    <author>Adam Schienle</author>
    <author>Thomas Schlechte</author>
    <author>Swen Schlobach</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="LHS-ATN">LHS-ATN</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5984</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>259</pageFirst>
    <pageLast>264</pageLast>
    <pageNumber/>
    <edition>Mathematical Software – ICMS 2016</edition>
    <issue/>
    <volume>9725</volume>
    <type>conferenceobject</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2016-07-06</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">PolySCIP</title>
    <abstract language="eng">PolySCIP is a new solver for multi-criteria integer and multi-criteria linear programs handling an arbitrary number of objectives. It is available as an official part of the non-commercial constraint integer programming framework SCIP. It utilizes a lifted weight space approach to compute the set of supported extreme non-dominated points and unbounded non-dominated rays, respectively. The algorithmic approach can be summarized as follows: At the beginning an arbitrary non-dominated point is computed (or it is determined that there is none) and a weight space polyhedron created. In every next iteration a vertex of the weight space polyhedron is selected whose entries give rise to a single-objective optimization problem via a combination of the original objectives. If the ptimization of this single-objective problem yields a new non-dominated point, the weight space polyhedron is updated. Otherwise another vertex of the weight space polyhedron is investigated. The algorithm finishes when all vertices of the weight space polyhedron have been investigated. The file format of PolySCIP is based on the widely used MPS format and allows a simple generation of multi-criteria models via an algebraic modelling language.</abstract>
    <parentTitle language="eng">Mathematical Software – ICMS 2016, 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings</parentTitle>
    <identifier type="isbn">978-3-319-42431-6</identifier>
    <identifier type="doi">10.1007/978-3-319-42432-3_32</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <editor>G.-M. Greuel</editor>
    <submitter>Sebastian Schenker</submitter>
    <author>Ralf Borndörfer</author>
    <editor>Thorsten Koch</editor>
    <author>Sebastian Schenker</author>
    <editor>Peter Paule</editor>
    <author>Martin Skutella</author>
    <editor>Andrew Sommese</editor>
    <author>Timo Strunk</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="mip">Mathematical Optimization Methods</collection>
    <collection role="institutes" number="traffic">Mathematics of Transportation and Logistics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MIP-ZIBOPT">MIP-ZIBOPT</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="CRC1026">CRC1026</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6007</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName>Springer-Verlag Berlin Heidelberg</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Passenger routing for periodic timetable optimization</title>
    <abstract language="eng">The task of periodic timetabling is to determine trip arrival and departure times in a public transport system such that travel and transfer times are minimized. This paper investigates periodic timetabling models with integrated passenger routing. We show that different routing models can have a huge influence on the quality of the entire system: Whatever metric is applied, the performance ratios of timetables w.r.t. different routing models can be arbitrarily large. Computations on a real-world instance for the city of Wuppertal substantiate the theoretical findings. These results indicate the existence of untapped optimization potentials that can be used to improve the efficiency of public transport systems by integrating passenger routing.</abstract>
    <parentTitle language="eng">Public Transport</parentTitle>
    <subTitle language="eng">Planning and Operations</subTitle>
    <identifier type="doi">10.1007/s12469-016-0132-0</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-56739</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Heide Hoppmann</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <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="hoppmann">Hoppmann, Heide</collection>
    <collection role="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6025</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>57</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Separation of Cycle Inequalities for the Periodic Timetabling Problem</title>
    <abstract language="eng">Cycle inequalities play an important role in the polyhedral study of the periodic timetabling problem. We give the first pseudo-polynomial time separation algorithm for cycle inequalities, and we give a rigorous proof for the pseudo-polynomial time separability of the change-cycle inequalities. The efficiency of these cutting planes is demonstrated on real-world instances of the periodic timetabling problem.</abstract>
    <parentTitle language="eng">24th Annual European Symposium on Algorithms (ESA 2016)</parentTitle>
    <identifier type="doi">10.4230/LIPIcs.ESA.2016.21</identifier>
    <enrichment key="Series">Leibniz International Proceedings in Informatics (LIPIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Heide Hoppmann</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <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="hoppmann">Hoppmann, Heide</collection>
    <collection role="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5575</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>56</pageFirst>
    <pageLast>73</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>18</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Metric inequalities for routings on direct connections with application to line planning</title>
    <abstract language="eng">We consider multi-commodity flow problems in which capacities are installed on paths. In this setting, it is often important to distinguish between flows on direct connection routes, using single paths, and flows that include path switching. We derive a feasibility condition for path capacities supporting such direct connection flows similar to the well-known feasibility condition for arc capacities in ordinary multi-commodity flows. The condition can be expressed in terms of a class of metric inequalities for routings on direct connections. We illustrate the concept on the example of the line planning problem in public transport and present an application to large-scale real-world problems.</abstract>
    <parentTitle language="eng">Discrete Optimization</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-53507</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Marika Karbstein</submitter>
    <author>Marika Karbstein</author>
    <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="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5578</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>127</pageFirst>
    <pageLast>132</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>40</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Sustainable Welding Process Selection based on Weight Space Partitions</title>
    <parentTitle language="eng">Procedia CIRP</parentTitle>
    <identifier type="doi">10.1016/j.procir.2016.01.077</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="Series">13th Global Conference on Sustainable Manufacturing - Decoupling Growth from Resource Use</enrichment>
    <author>Gunther Sprösser</author>
    <submitter>Sebastian Schenker</submitter>
    <author>Sebastian Schenker</author>
    <author>Andreas Pittner</author>
    <author>Ralf Borndörfer</author>
    <author>Michael Rethmeier</author>
    <author>Ya-Ju Chang</author>
    <author>Matthias Finkbeiner</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="CRC1026">CRC1026</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5579</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>276</pageFirst>
    <pageLast>280</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>26</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Modelling of Bicycle Manufacturing via Multi-criteria Mixed Integer Programming</title>
    <parentTitle language="eng">Procedia CIRP</parentTitle>
    <identifier type="doi">10.1016/j.procir.2014.07.068</identifier>
    <enrichment key="Series">12th Global Conference on Sustainable Manufacturing – Emerging Potentials</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Sebastian Schenker</author>
    <submitter>Sebastian Schenker</submitter>
    <author>Jón Garðar Steingrímsson</author>
    <author>Ralf Borndörfer</author>
    <author>Günther Seliger</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="CRC1026">CRC1026</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5577</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst>65</pageFirst>
    <pageLast>94</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>334</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Nachhaltige Technologiepfade für unterschiedliche Entwicklungsniveaus mithilfe mehrkriterieller Entscheidungsfindung</title>
    <parentTitle language="deu">Vorausschau und Technologieplanung</parentTitle>
    <identifier type="isbn">978-3-942647-53-3</identifier>
    <enrichment key="Series">10. Symposium für Vorausschau und Technologieplanung</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Pia Gausemeier</author>
    <submitter>Sebastian Schenker</submitter>
    <author>Günther Seliger</author>
    <author>Sebastian Schenker</author>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="CRC1026">CRC1026</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>4776</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>317</pageFirst>
    <pageLast>322</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An IP Approach to Toll Enforcement Optimization on German Motorways</title>
    <abstract language="eng">This paper proposes the first model for toll enforcement optimization on German motorways. The enforcement is done by mobile control teams and our goal is to produce a schedule achieving network-wide control, proportional to spatial and time-dependent traffic distributions. Our model consists of two parts. The first plans control tours using a vehicle routing approach with profits and some side constraints. The second plans feasible rosters for the control teams. Both problems can be modeled as Multi-Commodity Flow Problems. Adding additional coupling constraints produces a large-scale integrated integer programming formulation. We show that this model can be solved to optimality for real world instances associated with a control area in East Germany.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2011</parentTitle>
    <identifier type="doi">10.1007/978-3-642-29210-1_51</identifier>
    <enrichment key="Series">Operations Research Proceedings</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14299</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Elmar Swarat</submitter>
    <author>Guillaume Sagnol</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>4729</id>
    <completedYear/>
    <publishedYear>2013</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>253</pageFirst>
    <pageLast>260</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>41</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimizing Toll Enforcement in Transportation Networks: a Game-Theoretic Approach</title>
    <abstract language="eng">We present a game-theoretic approach to optimize the strategies of toll enforcement on a motorway network. In contrast to previous approaches, we consider a network with an arbitrary topology, and we handle the fact that users may choose their Origin-Destination path; in particular they may take a detour to avoid sections with a high control rate. We show that a Nash equilibrium can be computed with an LP (although the game is not zero-sum), and we give a MIP for the computation of a Stackelberg equilibrium. Experimental results based on an application to the enforcement of a truck toll on German motorways are presented.</abstract>
    <parentTitle language="eng">Proceedings of INOC'2013</parentTitle>
    <identifier type="doi">http://dx.doi.org//10.1016/j.endm.2013.05.100</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-17401</enrichment>
    <enrichment key="Series">Electronic Notes in Discrete Mathematics</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Elmar Swarat</submitter>
    <author>Julia Buwaya</author>
    <author>Guillaume Sagnol</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>4730</id>
    <completedYear/>
    <publishedYear>2012</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>224</pageFirst>
    <pageLast>235</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>105</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Stackelberg game to optimize the distribution of controls in transportation networks</title>
    <abstract language="eng">We propose a game theoretic model for the spatial distribution of inspectors on a transportation network. The problem is to spread out the controls so as to enforce the payment of a transit toll. We formulate a linear program to find the control distribution which maximizes the expected toll revenue, and a mixed integer program for the problem of minimizing the number of evaders. Furthermore, we show that the problem of finding an optimal mixed strategy for a coalition of $N$ inspectors can be solved efficiently by a column generation procedure. Finally, we give experimental results from an application to the truck toll on German motorways.</abstract>
    <parentTitle language="eng">Proceedings of the 3rd International Conference on Game Theory for Networks (GAMENETS 2012)</parentTitle>
    <identifier type="doi">http://dx.doi.org/10.1007/978-3-642-35582-0_17</identifier>
    <enrichment key="Series">Lecture Notes of the ICST</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14995</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Elmar Swarat</submitter>
    <author>Bertrand Omont</author>
    <author>Guillaume Sagnol</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5728</id>
    <completedYear>2015</completedYear>
    <publishedYear>2015</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">Recent Success Stories on Optimization of Railway Systems</title>
    <abstract language="eng">Planning and operating railway transportation systems is an extremely hard task due to the combinatorial complexity of the underlying discrete optimization problems, the technical intricacies, and the immense size of the problem instances. Because of that, however, mathematical models and optimization techniques can result in large gains for both railway cus- tomers and operators, e.g., in terms of cost reductions or service quality improvements. In the last years a large and growing group of researchers in the OR community have devoted their attention to this domain devel- oping mathematical models and optimization approaches to tackle many of the relevant problems in the railway planning process. However, there is still a gap to bridge between theory and practice, with a few notable exceptions. In this paper we address three success stories, namely, long-term freight train routing (part I), mid-term rolling stock rotation planning (part II), and real-time train dispatching (part III). In each case, we describe real-life, successful implementations. We will dis- cuss the individual problem setting, survey the optimization literature, and focus on particular aspects addressed by the mathematical models. We demonstrate on concrete applications how mathematical optimization can support railway planning and operations. This gives proof that math- ematical optimization can support the planning of rolling stock resources. Thus, mathematical models and optimization can lead to a greater effi- ciency of railway operations and will serve as a powerful and innovative tool to meet recent challenges of the railway industry.</abstract>
    <parentTitle language="eng">Proceedings of the IAROR conference RailTokyo</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-53726</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Leonardo Lamorgese</author>
    <author>Torsten Klug</author>
    <author>Carlo Mannino</author>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="klug">Klug, Torsten</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="ROTOR">ROTOR</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5760</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>15</pageFirst>
    <pageLast>25</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>15</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The hypergraph assignment problem</title>
    <parentTitle language="eng">Discrete Optimization</parentTitle>
    <identifier type="doi">10.1016/j.disopt.2014.11.002</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-14822</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Regine Kossick</submitter>
    <author>Olga Heismann</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MATHEON-B22">MATHEON-B22</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5275</id>
    <completedYear>2014</completedYear>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>51</pageFirst>
    <pageLast>68</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>226</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2014-08-21</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Fair ticket pricing in public transport as a constrained cost allocation game</title>
    <abstract language="eng">Ticket pricing in public transport usually takes a welfare maximization point of view. Such an approach, however, does not consider fairness in the sense that users of a shared infrastructure should pay for the costs that they generate. We propose an ansatz to determine fair ticket prices that combines concepts from cooperative game theory and linear and integer programming. The ticket pricing problem is considered to be a constrained cost allocation game, which is a generalization of cost allocation games that allows to deal with constraints on output prices and on the formation of coalitions. An application to pricing railway tickets for the intercity network of the Netherlands is presented. The results demonstrate that the fairness of prices can be improved substantially in this way.&#13;
&#13;
A preliminary version of this paper appeared in the Proceedings of HPSC 2009 (Borndörfer and Hoang 2012). This journal article introduces better model and algorithms.</abstract>
    <parentTitle language="eng">Annals of Operations Research</parentTitle>
    <identifier type="doi">10.1007/s10479-014-1698-z</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Regine Kossick</submitter>
    <author>Nam-Dung Hoang</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="ZIB-CostShare">ZIB-CostShare</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5136</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>49</pageFirst>
    <pageLast>55</pageLast>
    <pageNumber/>
    <edition>Operations Research Proceedings 2013</edition>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Re-Optimization of Rolling Stock Rotations</title>
    <abstract language="eng">The Rolling Stock Rotation Problem is to schedule rail vehicles in order to cover timetabled trips by a cost optimal set of vehicle rotations. The problem integrates several facets of railway optimization, such as vehicle composition, maintenance constraints, and regularity aspects. In industrial applications existing vehicle rotations often have to be re-optimized to deal with timetable changes or construction sites. We present an integrated modeling and algorithmic approach to this task as well as computational results for industrial problem instances of DB Fernverkehr AG.</abstract>
    <identifier type="doi">10.1007/978-3-319-07001-8_8</identifier>
    <enrichment key="Series">Operations Research Proceedings 2013</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-42569</enrichment>
    <submitter>Thomas Schlechte</submitter>
    <author>Ralf Borndörfer</author>
    <author>Julika Mehrgardt</author>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <author>Kerstin Waas</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="ROTOR">ROTOR</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5102</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>193</pageFirst>
    <pageLast>199</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Generalization of Odd Set Inequalities for the Set Packing Problem</title>
    <abstract language="eng">The set packing problem, sometimes also called the stable set problem, is a well-known NP-hard problem in combinatorial optimization with a wide range of applications and an interesting polyhedral structure, that has been the subject of intensive study. We contribute to this field by showing how, employing cliques, odd set inequalities for the matching problem can be generalized to valid inequalities for the set packing polytope with a clear combinatorial meaning.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2013</parentTitle>
    <identifier type="doi">10.1007/978-3-319-07001-8_26</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-51010</enrichment>
    <author>Olga Heismann</author>
    <submitter>Olga Heismann</submitter>
    <author>Ralf Borndörfer</author>
    <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="projects" number="MATHEON-B22">MATHEON-B22</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5367</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>312</pageFirst>
    <pageLast>328</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>65</volume>
    <type>article</type>
    <publisherName>Wiley Periodicals, Inc.</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Network spot-checking games: Theory and application to toll enforcing in transportation networks</title>
    <abstract language="eng">We introduce the class of spot-checking games (SC games). These games model problems where the goal is to distribute fare inspectors over a toll network. In an SC game, the pure strategies of network users correspond to paths in a graph, and the pure strategies of the inspectors are subset of arcs to be controlled. Although SC games are not zero-sum, we show that a Nash equilibrium can be computed by linear programming. The computation of a strong Stackelberg equilibrium (SSE) is more relevant for this problem and we give a mixed integer programming (MIP) formulation for this problem. We show that the computation of such an equilibrium is NP-hard. More generally, we prove that it is NP-hard to compute a SSE in a polymatrix game, even if the game is pairwise zero-sum. Then, we give some bounds on the price of spite, which measures how the payoff of the inspector degrades when committing to a Nash equilibrium. Finally, we report computational experiments on instances constructed from real data, for an application to the enforcement of a truck toll in Germany. These numerical results show the efficiency of the proposed methods, as well as the quality of the bounds derived in this article.</abstract>
    <parentTitle language="eng">Networks</parentTitle>
    <identifier type="doi">10.1002/net.21596</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-47139</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Guillaume Sagnol</submitter>
    <author>Julia Buwaya</author>
    <author>Guillaume Sagnol</author>
    <author>Elmar Swarat</author>
    <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="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5276</id>
    <completedYear/>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>293</pageFirst>
    <pageLast/>
    <pageNumber>1</pageNumber>
    <edition/>
    <issue/>
    <volume>8768</volume>
    <type>conferenceobject</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Price of Spite in Spot-checking games</title>
    <abstract language="eng">We introduce the class of spot-checking games (SC games). These games model&#13;
problems where the goal is to distribute fare inspectors over a toll network.&#13;
Although SC games are not zero-sum, we show that a Nash equilibrium&#13;
can be computed by linear programming.&#13;
The computation of a strong Stackelberg equilibrium is&#13;
more relevant for this problem, but we show that this is NP-hard.&#13;
However, we give some bounds on the \emph{price of spite},&#13;
which measures how the&#13;
payoff of the inspector&#13;
degrades when committing to a Nash equilibrium. &#13;
Finally, we demonstrate the quality of these bounds for a real-world application,&#13;
namely the enforcement of a truck toll on German motorways.</abstract>
    <parentTitle language="eng">7th International Symposium on Algorithmic Game Theory (SAGT'2014)</parentTitle>
    <identifier type="isbn">978-3-662-44802-1</identifier>
    <identifier type="doi">10.1007/978-3-662-44803-8</identifier>
    <note>Brief Announcement included in Back Matter p. 293 following</note>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-52775</enrichment>
    <editor>Ron Lavi</editor>
    <submitter>Guillaume Sagnol</submitter>
    <author>Guillaume Sagnol</author>
    <author>Ralf Borndörfer</author>
    <author>Thomas Schlechte</author>
    <author>Elmar Swarat</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="sagnol">Sagnol, Guillaume</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6432</id>
    <completedYear/>
    <publishedYear>2017</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">Pattern Detection For Large-Scale Railway Timetables</title>
    <abstract language="eng">We consider railway timetables of our industrial partner DB Fernverkehr AG that operates the ICE high speed trains in the long-distance passenger railway network of Germany. Such a timetable covers a whole year with 364 days and, typically, includes more than 45,000 trips. A rolling stock rotation plan is not created for the whole timetable at once. Instead the timetable is divided into regular invariant sections and irregular deviations (e.g. for public holidays). A separate rotation plan with a weekly period can then be provided for each of the different sections of the timetable. We present an algorithmic approach to automatically recognize these sections. Together with the supplementing visualisation of the timetable this method has shown to be very relevant for our industrial partner.</abstract>
    <parentTitle language="eng">Proceedings of the IAROR conference RailLille</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-63390</enrichment>
    <author>Stanley Schade</author>
    <submitter>Stanley Schade</submitter>
    <author>Ralf Borndörfer</author>
    <author>Matthias Breuer</author>
    <author>Boris Grimm</author>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <author>Patrick Siebeneicher</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="persons" number="schade">Schade, Stanley</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5729</id>
    <completedYear>2015</completedYear>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2015-07-23</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Duty Rostering in Public Transport - Facing Preferences, Fairness, and Fatigue</title>
    <abstract language="eng">Duty rostering problems occur in different application contexts and come in different flavors. They give rise to very large scale integer programs which ypically have lots of solutions and extremely fractional LP relaxations. In such a situation, heuristics can be a viable algorithmic choice. We propose an mprovement method of the Lin-Kernighan type for the solution of duty rostering problems. We illustrate its versatility and solution quality on three different applications in public transit, vehicle routing, and airline rostering with a focus on the management of preferences, fairness, and fatigue, respectively.</abstract>
    <parentTitle language="eng">Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015)</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-56070</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <author>Christof Schulz</author>
    <author>Elmar Swarat</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="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="schulz">Schulz, Christof</collection>
    <collection role="persons" number="swarat">Swarat, Elmar</collection>
    <collection role="persons" number="weider">Weider, Steffen</collection>
    <collection role="projects" number="LHS-CS">LHS-CS</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="projects" number="VS-Rail">VS-Rail</collection>
    <collection role="projects" number="WS-OPT">WS-OPT</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6407</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2017-03-22</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Umsteigen ohne Warten</title>
    <abstract language="deu">Wir stellen einen mathematischen Optimierungsansatz zur Berechnung von periodischen Taktfahrplänen vor, bei dem die Umsteigezeiten unter Berücksichtigung des Passagierverhaltens minimiert werden. Wir untersuchen damit den Einfluss wichtiger Systemparameter und Verhaltensmuster auf die Beförderungsqualität.</abstract>
    <parentTitle language="deu">HEUREKA 2017</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-62006</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Marika Karbstein</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <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="hoppmann">Hoppmann, Heide</collection>
    <collection role="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5711</id>
    <completedYear/>
    <publishedYear>2016</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>863</pageFirst>
    <pageLast>877</pageLast>
    <pageNumber>15</pageNumber>
    <edition/>
    <issue>3</issue>
    <volume>50</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Integrated Optimization of Rolling Stock Rotations for Intercity Railways</title>
    <abstract language="eng">This paper proposes a highly integrated solution approach for rolling stock planning problems in the context of long distance passenger traffic between cities. The main contributions are a generic hypergraph-based mixed-integer programming model for the considered rolling stock rotation problem and an integrated algorithm for its solution. The newly developed algorithm is able to handle a large spectrum of industrial railway requirements, such as vehicle composition, maintenance constraints, infrastructure capacities, and regularity aspects. We show that our approach has the power to produce rolling stock rotations that can be implemented in practice. In this way, the rolling stock rotations at the largest German long distance operator Deutsche Bahn Fernverkehr AG could be optimized by an automated system utilizing advanced mathematical programming techniques.</abstract>
    <parentTitle language="eng">Transportation Science</parentTitle>
    <identifier type="doi">10.1287/trsc.2015.0633</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="FulltextUrl">http://pubsonline.informs.org/doi/abs/10.1287/trsc.2015.0633</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-16424</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <author>Kerstin Waas</author>
    <author>Steffen Weider</author>
    <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="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="weider">Weider, Steffen</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="ROTOR">ROTOR</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5725</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>343</pageFirst>
    <pageLast>348</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>50</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Path Avoiding Forbidden Pairs Polytope</title>
    <abstract language="eng">Given a directed, acyclic graph, a source and a sink node, and a set of forbidden pairs of arcs, the path avoiding forbidden pairs (PAFP) problem is to find a path that connects the source and sink nodes and contains at most one arc from each forbidden pair. The general version of the problem is NP-hard, but it becomes polynomially solvable for certain topological configurations of the pairs. We present the first polyhedral study of the PAFP problem. We introduce a new family of valid inequalities for the PAFP polytope and show that they are sufficient to provide a complete linear description in the special case where the forbidden pairs satisfy a disjointness property. Furthermore, we show that the number of facets of the PAFP polytope is exponential in the size of the graph, even for the case of a single forbidden pair.</abstract>
    <parentTitle language="eng">Electronic Notes in Discrete Mathematics</parentTitle>
    <identifier type="doi">10.1016/j.endm.2015.07.057</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Marco Blanco</author>
    <submitter>Nam-Dung Hoang</submitter>
    <author>Ralf Borndörfer</author>
    <author>Michael Brückner</author>
    <author>Nam-Dung Hoang</author>
    <author>Thomas Schlechte</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="brueckner">Brückner, Michael</collection>
    <collection role="projects" number="LHS-ATN">LHS-ATN</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6183</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>19</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName>Springer</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Template-based Re-optimization of Rolling Stock Rotations</title>
    <abstract language="eng">Rolling stock, i.e., the set of railway vehicles, is among the most&#13;
expensive and limited assets of a railway company and must be used&#13;
efficiently. We consider in this paper the re-optimization&#13;
problem to recover from unforeseen disruptions. We propose a&#13;
template concept that allows to recover cost minimal rolling&#13;
stock rotations from reference rotations under a large variety of&#13;
operational requirements. To this end, connection templates as&#13;
well as rotation templates are introduced and their&#13;
application within a rolling stock rotation planning model is&#13;
discussed. We present an implementation within the rolling stock rotation&#13;
optimization framework rotor and computational results for&#13;
scenarios provided by DB Fernverkehr AG, one of the &#13;
leading railway operators in Europe.</abstract>
    <parentTitle language="eng">Public Transport</parentTitle>
    <identifier type="doi">10.1007/s12469-017-0152-4</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Boris Grimm</author>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <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="grimm">Grimm, Boris</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="ROTOR">ROTOR</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>6188</id>
    <completedYear/>
    <publishedYear>2017</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>239</pageFirst>
    <pageLast>253</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>bookpart</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimisation Methods in Sustainable Manufacturing</title>
    <abstract language="eng">Sustainable manufacturing is driven by the insight that the focus on the economic dimension in current businesses and lifestyles has to be broadened to cover all three pillars of sustainability: economic development, social development, and environmental protection.</abstract>
    <parentTitle language="eng">Sustainable Manufacturing</parentTitle>
    <subTitle language="eng">Challenges, Solutions and Implementation Perspectives</subTitle>
    <identifier type="isbn">978-3-319-48514-0</identifier>
    <identifier type="doi">10.1007/978-3-319-48514-0_15</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Sebastian Schenker</author>
    <submitter>Sebastian Schenker</submitter>
    <editor>Rainer Stark</editor>
    <author>Ingmar Vierhaus</author>
    <editor>Günther Seliger</editor>
    <author>Ralf Borndörfer</author>
    <editor>Jérémy Bonvoisin</editor>
    <author>Armin Fügenschuh</author>
    <author>Martin Skutella</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="fuegenschuh">Fügenschuh, Armin</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-SynLab">MODAL-SynLab</collection>
    <collection role="projects" number="CRC1026">CRC1026</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5627</id>
    <completedYear/>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst>239</pageFirst>
    <pageLast>243</pageLast>
    <pageNumber/>
    <edition/>
    <issue>7</issue>
    <volume>68</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Neue Planungsinstrumente nutzen: Das Verkehrsangebot verbessern und Kosten sparen</title>
    <abstract language="deu">Wir illustrieren anhand des Liniennetzes der Stadt Potsdam das Potenzial mathematischer Methoden der Angebotsplanung. Wir zeigen, dass das "bestmögliche" Verkehrsangebot stark von planerischen Vorgaben beeinflusst wird, mit denen man die Erreichung unterschiedlicher und teilweise gegenläufiger Ziele steuern kann. Die Komplexität des Systems führt zum Auftreten von Rückkoppelungseffekten, die man nicht mit Hilfe von Daumenregeln beherrschen kann. Vielmehr ist der Einsatz moderner Planungsverfahren in einer interdisziplinären Zusammenarbeit von politischen Entscheidungsträgern, Verkehrsingenieuren und Mathematikern notwendig, um die aktuellen Herausforderungen in der Verkehrsplanung zu meistern. Der Artikel dokumentiert einen Beitrag zum 7. ÖPNV Innovationskongress des Ministeriums für Verkehr und Infrastruktur des Landes Baden-Württemberg, der vom 9.-11. März 2015 in Freiburg stattfand.</abstract>
    <parentTitle language="deu">Verkehr und Technik</parentTitle>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-55439</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Marika Karbstein</submitter>
    <author>Marika Karbstein</author>
    <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="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="projects" number="MATHEON-B15">MATHEON-B15</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5653</id>
    <completedYear>2015</completedYear>
    <publishedYear>2015</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2015-07-23</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Timetabling and Passenger Routing in Public Transport</title>
    <abstract language="eng">The task of timetabling is to schedule the trips in a public transport system by determining periodic arrival and departure times at every station. The goal is to provide a service that is both attractive for passengers and can be operated economically. To date, timetable optimization is generally done with respect to fixed passenger routes, i.e., it is assumed that passengers do not respond to changes in the timetable. This is unrealistic and ignores potentially valuable degrees of freedom. We investigate in this paper periodic timetabling models with integrated passenger routing. We propose several models that differ in the allowed passenger paths and the objectives. We compare these models theoretically and report on computations on real-world instances for the city of Wuppertal.</abstract>
    <parentTitle language="eng">Proceedings of Conference on Advanced Systems in Public Transport 2015 (CASPT2015)</parentTitle>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-55305</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Heide Hoppmann</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Passenger routing</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Periodic timetabling</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>Public transport</value>
    </subject>
    <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="hoppmann">Hoppmann, Heide</collection>
    <collection role="projects" number="ECMath-MI3">ECMath-MI3</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>5291</id>
    <completedYear>2014</completedYear>
    <publishedYear>2014</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>79</pageFirst>
    <pageLast>91</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>42</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Coarse-To-Fine Approach to the Railway Rolling Stock Rotation Problem</title>
    <abstract language="eng">We propose a new coarse-to-fine approach to solve certain linear programs by column generation. The problems that we address contain layers corresponding to different levels of detail, i.e., coarse layers as well as fine layers. These layers are utilized to design efficient pricing rules. In a nutshell, the method shifts the pricing of a fine linear program to a coarse counterpart. In this way, major decisions are taken in the coarse layer, while minor details are tackled within the fine layer. We elucidate our methodology by an application to a complex railway rolling stock rotation problem. We provide comprehensive computational results that demonstrate the benefit of this new technique for the solution of large scale problems.</abstract>
    <parentTitle language="eng">14th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2014.79</identifier>
    <enrichment key="Series">OpenAccess Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-51009</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Markus Reuther</submitter>
    <author>Markus Reuther</author>
    <author>Thomas Schlechte</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="ROTOR">ROTOR</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>9643</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>259</pageFirst>
    <pageLast>276</pageLast>
    <pageNumber>17</pageNumber>
    <edition/>
    <issue/>
    <volume>14742</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ULD Build-Up Scheduling with Logic-Based Benders Decomposition</title>
    <abstract language="eng">We study a complex planning and scheduling problem arising from the build-up process of air cargo pallets and containers, collectively referred to as unit load devices (ULD), in which ULDs must be assigned to workstations for loading. Since air freight usually becomes available gradually along the planning horizon, ULD build-ups must be scheduled neither too early to avoid underutilizing ULD capacity, nor too late to avoid resource conflicts with other flights. Whenever possible, ULDs should be built up in batches, thereby giving ground handlers more freedom to rearrange cargo and utilize the ULD's capacity efficiently. The resulting scheduling problem has an intricate cost function and produces large time-expanded models, especially for longer planning horizons. We propose a logic-based Benders decomposition approach that assigns batches to time intervals and workstations in the master problem, while the actual schedule is decided in a subproblem. By choosing appropriate intervals, the subproblem becomes a feasibility problem that decomposes over the workstations. Additionally, the similarity of many batches is exploited by a strengthening procedure for no-good cuts. We benchmark our approach against a time-expanded MIP formulation from the literature on a publicly available data set. It solves 15% more instances to optimality and decreases run times by more than 50% in the geometric mean. This improvement is especially pronounced for longer planning horizons of up to one week, where the Benders approach solves over 50% instances more than the baseline</abstract>
    <parentTitle language="eng">Integration of Constraint Programming, Artificial Intelligence, and Operations Research</parentTitle>
    <identifier type="doi">10.1007/978-3-031-60597-0_17</identifier>
    <enrichment key="Series">Lecture Notes in Computer Science</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">02.02.2024</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ricardo Euler</author>
    <submitter>Ricardo Euler</submitter>
    <author>Ralf Borndörfer</author>
    <author>Christian Puchert</author>
    <author>Tuomo Takkula</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="euler">Euler, Ricardo</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="Cargo">Cargo</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8069</id>
    <completedYear>2021</completedYear>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst>1</pageFirst>
    <pageLast>15</pageLast>
    <pageNumber>15</pageNumber>
    <edition/>
    <issue/>
    <volume>002/127</volume>
    <type>article</type>
    <publisherName>FGSV</publisherName>
    <publisherPlace>Stuttgart</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-04-13</completedDate>
    <publishedDate>2021-04-13</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">Ein  Graphen-basiertes  Modell  zur  Beschreibung  von Preissystemen im öffentlichen Nahverkehr</title>
    <abstract language="deu">In dieser Arbeit wird ein graphenbasiertes Modell zur Einbindung von Preissystemen des öffentlichen Nahverkehrs in Routing-Algorithmen vorgestellt. Jeder Knoten des Graphen repräsentiert einen abstrakten Preiszustand einer Route und ist an einen tatsächlichen Preis gekoppelt. Damit sind sehr einfache und konzise Beschreibungen von Tarifstrukturen möglich, diesich algorithmisch behandeln lassen. Durch das zeitgleiche Tracken eines Pfades im Routinggraphen im Ticketgraphen kann schon während einer Routenberechnung der Preis bestimmt werden. Dies ermöglicht die Berechnung von preisoptimalen Routen. An den Tarifsystemen der Verkehrsverbünde MDV (Mitteldeutscher Verkehrsverbund) und VBB (Verkehrsverbund Berlin-Brandenburg) wird die Konstruktion des Modells detailliert erläutert.</abstract>
    <parentTitle language="deu">HEUREKA 21</parentTitle>
    <identifier type="url">https://verlag.fgsv-datenbanken.de/tagungsbaende?kat=HEUREKA&amp;subkat=FGSV+002%2F127+%282021%29&amp;fanr=&amp;va=&amp;titel=&amp;text=&amp;autor=&amp;tagungsband=1256&amp;_titel=Ein+Graphen-basiertes+Modell+zur+Beschreibung+von+Preissystemen+im+%C3%B6ffentlichen+Nahverkehr</identifier>
    <enrichment key="Series">FGSV Heureka</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Ricardo Euler</submitter>
    <author>Ricardo Euler</author>
    <author>Marika Karbstein</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="euler">Euler, Ricardo</collection>
    <collection role="projects" number="MOIN">MOIN</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>9797</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>other</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-07-19</completedDate>
    <publishedDate>2024-07-19</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Electric Bus Scheduling with Non-Linear Charging, Power Grid Bottlenecks, and Dynamic Recharge Rates</title>
    <abstract language="eng">Public transport operators are gradually electrifying their bus fleets, predominantly with battery-powered drive trains. These buses commonly have to be scheduled to recharge in-service, which gives rise to a number of challenges. A major problem is that the relationship between charging time and replenished driving range is non-linear, which is often approximately modeled. We examine the associated approximation error and show how it can result in a gross over- or underestimation of the fleet size. Moreover, we demonstrate that commonly used piecewise linear underestimations of the charge curve do not result in an underestimation of the predicted charge states in electric vehicle scheduling and routing models.&#13;
Furthermore, since power grid upgrades are currently not keeping up with an ever growing electricity demand, operators are introducing active charge management tools to dynamically adjust the charging speed depending on the amount of available energy. It is therefore imperative to extend electric bus scheduling models to account for these developments.&#13;
We propose a novel mixed-integer programming formulation for the electric bus scheduling problem featuring an improved approximation of the non-linear battery charging behavior as well as dynamic recharge speeds to accommodate grid load limits. The idea is to linearly interpolate what we call the charge increment function, which is closely related to the derivative of the commonly used charge curve. This provides very good error control and integrates easily into integer programming models. We demonstrate the practical usefulness of our model on a diverse library of real-life instances.</abstract>
    <identifier type="arxiv">2407.14446</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Fabian Löbel</author>
    <submitter>Fabian Löbel</submitter>
    <author>Ralf Borndörfer</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="weider">Weider, Steffen</collection>
    <collection role="persons" number="fabian.loebel">Löbel, Fabian</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="EBUS">EBUS</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>9795</id>
    <completedYear>2024</completedYear>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>11:1</pageFirst>
    <pageLast>11:16</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>123</volume>
    <type>conferenceobject</type>
    <publisherName>Schloss Dagstuhl -- Leibniz-Zentrum für Informatik</publisherName>
    <publisherPlace>Dagstuhl, Germany</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-10-07</completedDate>
    <publishedDate>2024-10-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Solving the Electric Bus Scheduling Problem by an Integrated Flow and Set Partitioning Approach</title>
    <abstract language="eng">Attractive and cost-efficient public transport requires solving computationally difficult optimization problems from network design to crew rostering. While great progress has been made in many areas, new requirements to handle increasingly complex constraints are constantly coming up. One such challenge is a new type of resource constraints that are used to deal with the state-of-charge of battery-electric vehicles, which have limited driving ranges and need to be recharged in-service. Resource constrained vehicle scheduling problems can classically be modelled in terms of either a resource constrained (multi-commodity) flow problem or in terms of a path-based set partition problem. We demonstrate how a novel integrated version of both formulations can be leveraged to solve resource constrained vehicle scheduling with replenishment in general and the electric bus scheduling problem in particular by Lagrangian relaxation and the proximal bundle method.</abstract>
    <parentTitle language="eng">24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2024.11</identifier>
    <identifier type="urn">urn:nbn:de:0030-drops-211992</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-08-07</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <submitter>Fabian Löbel</submitter>
    <author>Ralf Borndörfer</author>
    <author>Andreas Löbel</author>
    <author>Fabian 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="loebel">Löbel, Andreas</collection>
    <collection role="persons" number="weider">Weider, Steffen</collection>
    <collection role="persons" number="fabian.loebel">Löbel, Fabian</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="EBUS">EBUS</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>9602</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Iterative Refinement Approach for the Rolling Stock Rotation Problem with Predictive Maintenance</title>
    <abstract language="eng">The rolling stock rotation problem with predictive maintenance (RSRP-PdM) involves the assignment of trips to a fleet of vehicles with integrated maintenance scheduling based on the predicted failure probability of the vehicles. These probabilities are determined by the health states of the vehicles, which are considered to be random variables distributed by a parameterized family of probability distribution functions. During the operation of the trips, the corresponding parameters get updated. In this article, we present a dual solution approach for RSRP-PdM and generalize a linear programming based lower bound for this problem to families of probability distribution functions with more than one parameter. For this purpose, we define a rounding function that allows for a consistent underestimation of the parameters and model the problem by a state-expanded event-graph in which the possible states are restricted to a discrete set. This induces a flow problem that is solved by an integer linear program. We show that the iterative refinement of the underlying discretization leads to solutions that converge from below to an optimal solution of the original instance. Thus, the linear relaxation of the considered integer linear program results in a lower bound for RSRP-PdM. Finally, we report on the results of computational experiments conducted on a library of test instances.</abstract>
    <identifier type="arxiv">2404.08367</identifier>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PeerReviewed">no</enrichment>
    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="prause">Prause, Felix</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="BerDiBa">BerDiBa</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>9556</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>100434</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>30</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approximating rolling stock rotations with integrated predictive maintenance</title>
    <abstract language="eng">We study the solution of the rolling stock rotation problem with predictive maintenance (RSRP-PdM) by an iterative refinement approach that is based on a state-expanded event-graph. In this graph, the states are parameters of a failure distribution, and paths correspond to vehicle rotations with associated health state approximations. An optimal set of paths including maintenance can be computed by solving an integer linear program. Afterwards, the graph is refined and the procedure repeated. An associated linear program gives rise to a lower bound that can be used to determine the solution quality. Computational results for six instances derived from real-world timetables of a German railway company are presented. The results show the effectiveness of the approach and the quality of the solutions.</abstract>
    <parentTitle language="eng">Journal of Rail Transport Planning &amp; Management</parentTitle>
    <identifier type="doi">10.1016/j.jrtpm.2024.100434</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2024-02-28</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-89531</enrichment>
    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <author>Boris Grimm</author>
    <author>Alexander Tesch</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="persons" number="tesch">Tesch, Alexander</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="prause">Prause, Felix</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="BerDiBa">BerDiBa</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8406</id>
    <completedYear>2021</completedYear>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>17:1</pageFirst>
    <pageLast>17:6</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>96</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-09-27</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Efficient Algorithms for the Multi-Period Line Planning Problem in Public Transportation</title>
    <abstract language="eng">In order to plan and schedule a demand-responsive public transportation system, both temporal and spatial changes in demand should be taken into account even at the line planning stage. We study the multi-period line planning problem with integrated decisions regarding dynamic allocation of vehicles among the lines. Given the NP-hard nature of the line planning problem, the multi-period version is clearly difficult to solve for large public transit networks even with advanced solvers. It becomes necessary to develop algorithms that are capable of solving even the very-large instances in reasonable time. For instances which belong to real public transit networks, we present results of a heuristic local branching algorithm and an exact approach based on constraint propagation.</abstract>
    <parentTitle language="eng">Open Access Series in Informatics (OASIcs), 21st Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2021)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2021.17</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Guvenc Sahin</author>
    <submitter>Ralf Borndörfer</submitter>
    <author>Amin Ahmadi Digehsara</author>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8099</id>
    <completedYear>2020</completedYear>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>4</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>14</volume>
    <type>article</type>
    <publisherName>MDPI</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2020-12-25</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Discrete-Continuous Algorithm for Free Flight Planning</title>
    <abstract language="eng">We propose a hybrid discrete-continuous algorithm for flight planning in free flight airspaces. In a first step, our DisCOptER method discrete-continuous optimization for enhanced resolution) computes a globally optimal approximate flight path on a discretization of the problem using the A* method. This route initializes a Newton method that converges rapidly to the smooth optimum in a second step. The correctness, accuracy, and complexity of the method are goverened by the choice of the crossover point that determines the coarseness of the discretization. We analyze the optimal choice of the crossover point and demonstrate the asymtotic superority of DisCOptER over a purely discrete approach.</abstract>
    <parentTitle language="eng">Algorithms</parentTitle>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="doi">10.3390/a14010004</identifier>
    <enrichment key="AcceptedDate">2020-12-20</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-81343</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>shortest path</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>flight planning</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>free flight</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete-continuous algorithm</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>optimal control</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>discrete optimization</value>
    </subject>
    <collection role="msc" number="49M37">Methods of nonlinear programming type [See also 90C30, 65Kxx]</collection>
    <collection role="msc" number="65K10">Optimization and variational techniques [See also 49Mxx, 93B40]</collection>
    <collection role="msc" number="65L10">Boundary value problems</collection>
    <collection role="msc" number="90C27">Combinatorial optimization</collection>
    <collection role="msc" number="90C35">Programming involving graphs or networks [See also 90C27]</collection>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MfLMS">Mathematics for Life and Materials Science</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="Mathematical Algorithmic Intelligence">Mathematical Algorithmic Intelligence</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8041</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>42</pageFirst>
    <pageLast>62</pageLast>
    <pageNumber/>
    <edition/>
    <issue>1</issue>
    <volume>51</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation>Institute for Operations Research and the Management Sciences (INFORMS)</contributingCorporation>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2021-02-10</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Deutsche Bahn Schedules Train Rotations Using Hypergraph Optimization</title>
    <abstract language="eng">Deutsche Bahn (DB) operates a large fleet of rolling stock (locomotives, wagons, and train sets) that must be combined into trains to perform rolling stock rotations. This train composition is a special characteristic of railway operations that distinguishes rolling stock rotation planning from the vehicle scheduling problems prevalent in other industries. DB models train compositions using hyperarcs. The resulting hypergraph models are ad-dressed using a novel coarse-to-fine method that implements a hierarchical column genera-tion over three levels of detail. This algorithm is the mathematical core of DB’s fleet em-ployment optimization (FEO) system for rolling stock rotation planning. FEO’s impact within DB’s planning departments has been revolutionary. DB has used it to support the company’s procurements of its newest high-speed passenger train fleet and its intermodal cargo locomotive fleet for cross-border operations. FEO is the key to successful tendering in regional transport and to construction site management in daily operations. DB’s plan-ning departments appreciate FEO’s high-quality results, ability to reoptimize (quickly), and ease of use. Both employees and customers benefit from the increased regularity of operations. DB attributes annual savings of 74 million euro, an annual reduction of 34,000 tons of CO2 emissions, and the elimination of 600 coupling operations in cross-border operations to the implementation of FEO.</abstract>
    <parentTitle language="eng">Informs Journal on Applied Analytics</parentTitle>
    <identifier type="doi">10.1287/inte.2020.1069</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2020-11-05</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Ralf Borndörfer</submitter>
    <author>Thomas Eßer</author>
    <author>Patrick Frankenberger</author>
    <author>Andreas Huck</author>
    <author>Christoph Jobmann</author>
    <author>Boris Krostitz</author>
    <author>Karsten Kuchenbecker</author>
    <author>Kai Moorhagen</author>
    <author>Philipp Nagl</author>
    <author>Michael Peterson</author>
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    <title language="eng">Logic-Constrained Shortest Paths for Flight Planning</title>
    <abstract language="eng">The Logic-Constrained Shortest Path Problem (LCSP) combines a one-to-one shortest path problem with satisfiability constraints imposed on the routing graph. This setting arises in flight planning, where air traffic control (ATC) authorities are enforcing a set of traffic flow restrictions (TFRs) on aircraft routes in order to increase safety and throughput. We propose a new branch and bound-based algorithm for the LCSP. The resulting algorithm has three main degrees of freedom: the node selection rule, the branching rule and the conflict. While node selection and branching rules have been long studied in the MIP and SAT communities, most of them cannot be applied out of the box for the LCSP. We review the existing literature and develop tailored variants of the most prominent rules. The conflict, the set of variables to which the branching rule is applied, is unique to the LCSP. We analyze its theoretical impact on the B&amp;B algorithm. In the second part of the paper, we show how to model the Flight Planning Problem with TFRs as an LCSP and solve it using the branch and bound algorithm. We demonstrate the algorithm’s efficiency on a dataset consisting of a global flight graph and a set of around 20000 real TFRs obtained from our industry partner Lufthansa Systems GmbH. We make this dataset publicly available. Finally, we conduct an empirical in-depth analysis of node selection rules, branching rules and conflicts. Carefully choosing an appropriate combination yields an improvement of an order of magnitude compared to an uninformed choice.</abstract>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Improved Multiobjective Shortest Path Algorithm</title>
    <abstract language="eng">We present a new label-setting algorithm for the Multiobjective Shortest Path (MOSP) problem that computes a minimum complete set of efficient paths for a given instance. The size of the priority queue used in the algorithm is bounded by the number of nodes in the input graph and extracted labels are guaranteed to be efficient. These properties allow us to give a tight output-sensitive running time bound for the new algorithm that can almost be expressed in terms of the running time of Dijkstra’s algorithm for the Shortest Path problem. Hence, we suggest to call the algorithm Multiobjective Dijkstra Algorithm (MDA). The simplified label management in the MDA allows us to parallelize some subroutines. In our computational experiments, we compare the MDA and the classical label-setting MOSP algorithm by Martins, which we improved using new data structures and pruning techniques. On average, the MDA is 2 to 9 times faster on all used graph types. On some instances the speedup reaches an order of magnitude.</abstract>
    <parentTitle language="eng">Computers &amp; Operations Research</parentTitle>
    <identifier type="doi">10.1016/j.cor.2021.105424</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-79712</enrichment>
    <author>Pedro Maristany de las Casas</author>
    <submitter>Ekaterina Engel</submitter>
    <author>Antonio Sedeno-Noda</author>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="LHS-ATN">LHS-ATN</collection>
    <collection role="persons" number="maristany">Maristany de las Casas, Pedro</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>8407</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>100315</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>22</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Timetable Optimization for a Moving Block System</title>
    <abstract language="eng">We present an optimization model which is capable of routing and ordering trains on a microscopic level under a moving block regime. Based on a general timetabling definition (GTTP) that allows the plug in of arbitrarily detailed methods to compute running and headway times, we describe a layered graph approach using velocity expansion, and develop a mixed integer linear programming formulation. Finally, we present promising results for a German corridor scenario with mixed traffic, indicating that applying branch-and-cut to our model is able to solve reasonably sized instances with up to hundred trains to optimality.</abstract>
    <parentTitle language="eng">Journal of Rail Transport Planning &amp; Management</parentTitle>
    <identifier type="doi">10.1016/j.jrtpm.2022.100315</identifier>
    <identifier type="issn">2210-9706</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-03-25</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-82547</enrichment>
    <author>Thomas Schlechte</author>
    <submitter>Niels Lindner</submitter>
    <author>Ralf Borndörfer</author>
    <author>Jonas Denißen</author>
    <author>Simon Heller</author>
    <author>Torsten Klug</author>
    <author>Michael Küpper</author>
    <author>Niels Lindner</author>
    <author>Markus Reuther</author>
    <author>Andreas Söhlke</author>
    <author>William Steadman</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="klug">Klug, Torsten</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="reuther">Reuther, Markus</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8205</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>22</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>14</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An FPTAS for Dynamic Multiobjective Shortest Path Problems</title>
    <abstract language="eng">The Dynamic Multiobjective Shortest Path problem features multidimensional costs that can depend on several variables and not only on time; this setting is motivated by flight planning applications and the routing of electric vehicles. We give an exact algorithm for the FIFO case and derive from it an FPTAS for both, the static Multiobjective Shortest Path (MOSP) problems and, under mild assumptions, for the dynamic problem variant. The resulting FPTAS is computationally efficient and beats the known complexity bounds of other FPTAS for MOSP problems.</abstract>
    <parentTitle language="eng">Algorithms</parentTitle>
    <identifier type="doi">https://doi.org/10.3390/a14020043</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-01-22</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-80954</enrichment>
    <licence>Creative Commons - CC BY - Namensnennung 4.0 International</licence>
    <author>Pedro Maristany de las Casas</author>
    <submitter>Pedro Maristany de las Casas</submitter>
    <author>Ralf Borndörfer</author>
    <author>Luitgard Kraus</author>
    <author>Antonio Sedeño-Noda</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="LHS-ATN">LHS-ATN</collection>
    <collection role="persons" number="maristany">Maristany de las Casas, Pedro</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8641</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Price Optimal Routing in Public Transportation</title>
    <abstract language="eng">We consider the price-optimal earliest arrival problem in public transit (POEAP) in which we aim to calculate the Pareto-front of journeys with respect to ticket price and arrival time in a public transportation network. Public transit fare structures are often a combination of various fare strategies such as, e.g., distance-based fares, zone-based fares or flat fares. The rules that determine the actual ticket price are often very complex. Accordingly, fare structures are notoriously difficult to model as it is in general not sufficient to simply assign costs to arcs in a routing graph. Research into POEAP is scarce and usually either relies on heuristics or only considers restrictive fare models that are too limited to cover the full scope of most real-world applications. We therefore introduce conditional fare networks (CFNs), the first framework for representing a large number of real-world fare structures. We show that by relaxing label domination criteria, CFNs can be used as a building block in label-setting multi-objective shortest path algorithms. By the nature of their extensive modeling capabilities, optimizing over CFNs is NP-hard. However, we demonstrate that adapting the multi-criteria RAPTOR (MCRAP) algorithm for CFNs yields an algorithm capable of solving POEAP to optimality in less than 400 ms on average on a real-world data set. By restricting the size of the Pareto-set, running times are further reduced to below 10 ms.</abstract>
    <identifier type="doi">https://doi.org/10.48550/arXiv.2204.01326</identifier>
    <identifier type="arxiv">2204.01326</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-86414</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ricardo Euler</author>
    <submitter>Ricardo Euler</submitter>
    <author>Niels Lindner</author>
    <author>Ralf Borndörfer</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="euler">Euler, Ricardo</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="projects" number="MOIN">MOIN</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8781</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>254</pageFirst>
    <pageLast>260</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-08-30</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">ULD Build-Up Scheduling with Dynamic Batching in an Air Freight Hub</title>
    <abstract language="eng">Air freight is usually shipped in standardized unit load devices (ULDs). The planning process for the consolidation of transit cargo from inbound flights or locally emerging shipments into ULDs for outbound flights is called build-up scheduling. More specifically, outbound ULDs must be assigned a time and a workstation subject to both workstation capacity constraints and the availability of shipments which in turn depends on break-down decisions for incoming ULDs. ULDs scheduled for the same outbound flight should be built up in temporal and spatial proximity. This serves both to minimize overhead in transportation times and to allow workers to move freight between ULDs. We propose to address this requirement by processing ULDs for the same outbound flight in batches.&#13;
For the above build-up scheduling problem, we introduce a multi-commodity network design model. Outbound flights are modeled as commodities; transit cargo is represented by cargo flow volume and unpack and batch decisions are represented as design variables. The model is solved with a standard MIP solver on a set of benchmark data. For instances with a limited number of resource conflicts, near-optimal solutions are found in under two hours for a whole week of operations.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2021</parentTitle>
    <identifier type="doi">10.1007/978-3-031-08623-6_38</identifier>
    <enrichment key="Series">Lecture Notes in Operations Research</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2021-12-09</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-83482</enrichment>
    <author>Ricardo Euler</author>
    <submitter>Ricardo Euler</submitter>
    <author>Ralf Borndörfer</author>
    <author>Timo Strunk</author>
    <author>Tuomo Takkula</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="euler">Euler, Ricardo</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="Cargo">Cargo</collection>
  </doc>
  <doc>
    <id>8573</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>277</pageFirst>
    <pageLast>298</pageLast>
    <pageNumber/>
    <edition/>
    <issue>3</issue>
    <volume>82</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-07-08</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Targeted multiobjective Dijkstra Algorithm</title>
    <abstract language="eng">We introduce the Targeted Multiobjective Dijkstra Algorithm (T-MDA), a label setting algorithm for the One-to-One Multiobjective Shortest Path (MOSP) Problem. It is based on the recently published Multiobjective Dijkstra Algorithm (MDA) and equips it with A*-like techniques. For any explored subpath, a label setting MOSP algorithm decides whether the subpath can be discarded or must be stored as part of the output. A major design choice is how to store subpaths from the moment they are first explored until the mentioned final decision can be made. The T-MDA combines the polynomially bounded size of the priority queue used in the MDA and alazy management of paths that are not in the queue. The running time bounds from the MDA remain valid. In practice, the T-MDA outperforms known algorithms from the literature and the increased memory consumption is negligible. In this paper, we benchmark the T-MDA against an improved version of the state of the art NAMOA∗drOne-to-One MOSP algorithm from the literature on a standard testbed.</abstract>
    <parentTitle language="eng">Networks</parentTitle>
    <identifier type="arxiv">2110.10978</identifier>
    <identifier type="doi">10.1002/net.22174</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Pedro Maristany de las Casas</author>
    <submitter>Pedro Maristany de las Casas</submitter>
    <author>Luitgard Kraus</author>
    <author>Antonio Sedeno-Noda</author>
    <author>Ralf Borndörfer</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="LHS-ATN">LHS-ATN</collection>
    <collection role="persons" number="maristany">Maristany de las Casas, Pedro</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8964</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>295</pageFirst>
    <pageLast>301</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer, Cham</publisherName>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2022-08-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs</title>
    <abstract language="eng">Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC,  we observe that the two cost functions are qualitatively comparable.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2021</parentTitle>
    <identifier type="isbn">978-3-031-08623-6</identifier>
    <identifier type="doi">10.1007/978-3-031-08623-6_44</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-84195</enrichment>
    <enrichment key="Series">Lecture Notes in Operations Research</enrichment>
    <editor>Norbert Trautmann</editor>
    <submitter>Berenike Masing</submitter>
    <author>Berenike Masing</author>
    <editor>Mario Drägi</editor>
    <author>Niels Lindner</author>
    <author>Ralf Borndörfer</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="SymLPP">SymLPP</collection>
  </doc>
  <doc>
    <id>8866</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1:1</pageFirst>
    <pageLast>1:15</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>106</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An A* Algorithm for Flight Planning Based on Idealized Vertical Profiles</title>
    <abstract language="eng">The Flight Planning Problem is to find a minimum fuel trajectory between two airports in a 3D airway network under consideration of the wind. We show that this problem is NP-hard, even in its most basic version. We then present a novel A∗ heuristic, whose potential function is derived from an idealized vertical profile over the remaining flight distance. This potential is, under rather general assumptions, both admissible and consistent and it can be computed efficiently. The method outperforms the state-of-the-art heuristic on real-life instances.</abstract>
    <parentTitle language="eng">22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2022.1</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Marco Blanco</author>
    <submitter>Marco Blanco</submitter>
    <author>Ralf Borndörfer</author>
    <author>Pedro Maristany de las Casas</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="maristany">Maristany de las Casas, Pedro</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8861</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>deu</language>
    <pageFirst>419</pageFirst>
    <pageLast>443</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>166</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="deu">The price of symmetric line plans in the Parametric City</title>
    <abstract language="eng">We consider the line planning problem in public transport in the Parametric City, an idealized model that captures typical scenarios by a (small) number of parameters. The Parametric City is rotation symmetric, but optimal line plans are not always symmetric. This raises the question to quantify the symmetry gap between the best symmetric and the overall best solution. For our analysis, we formulate the line planning problem as a mixed integer linear program, that can be solved in polynomial time if the solutions are forced to be symmetric. We prove that the symmetry gap is small when a specific Parametric City parameter is fixed, and we give an approximation algorithm for line planning in the Parametric City in this case. While the symmetry gap can be arbitrarily large in general, we show that symmetric line plans are a good choice in most practical situations.</abstract>
    <parentTitle language="eng">Transportation Research Part B: Methodological</parentTitle>
    <identifier type="doi">10.1016/j.trb.2022.10.009</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-88613</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-85648</enrichment>
    <author>Berenike Masing</author>
    <submitter>Berenike Masing</submitter>
    <author>Niels Lindner</author>
    <author>Ralf Borndörfer</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="SymLPP">SymLPP</collection>
  </doc>
  <doc>
    <id>9293</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>13:1</pageFirst>
    <pageLast>13:15</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>115</volume>
    <type>conferenceobject</type>
    <publisherName>Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik</publisherName>
    <publisherPlace>Dagstuhl, Germany</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Assignment Based Resource Constrained Path Generation for Railway Rolling Stock Optimization</title>
    <abstract language="eng">The fundamental task of every passenger railway operator is to offer an attractive railway timetable to the passengers while operating it as cost efficiently as possible. The available rolling stock has to be assigned to trips so that all trips are operated, operational requirements are satisfied, and the operating costs are minimum. This so-called Rolling Stock Rotation Problem (RSRP) is well studied in the literature. In this paper we consider an acyclic version of the RSRP that includes vehicle maintenance. As the latter is an important aspect, maintenance services have to be planned simultaneously to ensure the rotation’s feasibility in practice. Indeed, regular maintenance is important for the safety and reliability of the rolling stock as well as enforced by law in many countries. We present a new integer programming formulation that links a hyperflow to model vehicle compositions and their coupling decisions to a set of path variables that take care of the resource consumption of the individual vehicles. To solve the model we developed different column generation algorithms which are compared to each other as well as to the MILP flow formulation of [Ralf Borndörfer et al., 2016] on a test set of real world instances.</abstract>
    <parentTitle language="eng">23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)</parentTitle>
    <identifier type="doi">https://doi.org/10.4230/OASIcs.ATMOS.2023.13</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">31.07.23</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="FulltextUrl">https://drops.dagstuhl.de/storage/01oasics/oasics-vol115-atmos2023/OASIcs.ATMOS.2023.13/OASIcs.ATMOS.2023.13.pdf</enrichment>
    <author>Boris Grimm</author>
    <submitter>Boris Grimm</submitter>
    <author>Ralf Borndörfer</author>
    <author>Julian Bushe</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>9294</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
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    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>CCC 1</volume>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Robustness Analysis of Long Distance Train Crew Schedules in Germany</title>
    <abstract language="eng">Nowadays railway networks are highly complex and often very fragile systems. A wide variety of individual operations that influence each other have to go hand in hand to end up with a smoothly and efficiently running system. Many of these operations suffer from uncertainty as trains could be delayed, the signaling system be disrupted or scheduled crews could be ill. Usually these opartions could be organized hierarchically from long term strategical decisions to real time decision management. Each stage in the hierarchy defines a different mathematical optimization problem, which is solved sequentially. At every stage the knowledge about preceding or succeeding planning stages may vary and also the interaction between two stages in this chain of problems may vary from almost no interaction to highly dependent situations. This paper deals with a topic that is an example for the latter case, namely the interaction between vehicle schedules, vehicle punctuality, and crew schedules. To reduce the number of potential rescheduling actions we developed a software tool in cooperation with our practical partner DB Fernverkehr AG (DBF) to predict a certain set of critical crew schedules. This tool evaluates, predicts, and determines "bottlenecks" in the crew schedule in the sense of potentially required rescheduling actions due to likely delays. The approach was tested on real life crew and train timetable data of DBF and can be regarded as the computation of key performance indicators, which is often desired. For our experiments we had access to the operated timetable and crew schedule of DBF for periods of two and six weeks in 2019.</abstract>
    <parentTitle language="eng">Proceedings Of The Fifth Iinternational Conference On Railway Technology: Research, Development and Maintenance</parentTitle>
    <identifier type="doi">10.4203/ccc.1.23.17</identifier>
    <identifier type="issn">2753-3239</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Boris Grimm</submitter>
    <author>Boris Grimm</author>
    <author>Stanley Schade</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="grimm">Grimm, Boris</collection>
    <collection role="projects" number="MODAL-RailLab">MODAL-RailLab</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>8083</id>
    <completedYear/>
    <publishedYear>2020</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>757</pageFirst>
    <pageLast>763</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName>Springer International Publishing</publisherName>
    <publisherPlace>Cham</publisherPlace>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">The Restricted Modulo Network Simplex Method for Integrated Periodic Timetabling and Passenger Routing</title>
    <abstract language="eng">The Periodic Event Scheduling Problem is a well-studied NP-hard problem with applications in public transportation to find good periodic timetables. Among the most powerful heuristics to solve the periodic timetabling problem is the modulo network simplex method. In this paper, we consider the more difficult version with integrated passenger routing and propose a refined integrated variant to solve this problem on real-world-based instances.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2019</parentTitle>
    <identifier type="doi">https://doi.org/10.1007/978-3-030-48439-2_92</identifier>
    <identifier type="isbn">978-3-030-48438-5</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-73868</enrichment>
    <author>Fabian Löbel</author>
    <submitter>Niels Lindner</submitter>
    <editor>Janis S. Neufeld</editor>
    <author>Niels Lindner</author>
    <editor>Udo Buscher</editor>
    <author>Ralf Borndörfer</author>
    <editor>Rainer Lasch</editor>
    <editor>Dominik Möst</editor>
    <editor>Jörn Schönberger</editor>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="fabian.loebel">Löbel, Fabian</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="projects" number="ECMath-MI7">ECMath-MI7</collection>
    <collection role="projects" number="MathPlus-Incubator-Timetabling">MathPlus-Incubator-Timetabling</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
  </doc>
  <doc>
    <id>9505</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>106186</pageFirst>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>154</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2023-02-24</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A three-phase heuristic for the Fairness-Oriented Crew Rostering Problem</title>
    <abstract language="eng">The Fairness-Oriented Crew Rostering Problem (FCRP) considers the joint optimization of attractiveness and fairness in cyclic crew rostering. Like many problems in scheduling and logistics, the combinatorial complexity of cyclic rostering causes exact methods to fail for large-scale practical instances. In case of the FCRP, this is accentuated by the additionally imposed fairness requirements. Hence, heuristic methods are necessary. We present a three-phase heuristic for the FCRP combining column generation techniques with variable-depth neighborhood search. The heuristic exploits different mathematical formulations to find feasible solutions and to search for improvements. We apply our methodology to practical instances from Netherlands Railways (NS), the main passenger railway operator in the Netherlands Our results show the three-phase heuristic finds good solutions for most instances and outperforms a state-of-the-art commercial solver.</abstract>
    <parentTitle language="eng">Computers &amp; Operations Research</parentTitle>
    <identifier type="doi">10.1016/j.cor.2023.106186</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="SubmissionStatus">epub ahead of print</enrichment>
    <enrichment key="AcceptedDate">2023-03-06</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Thomas Breugem</author>
    <submitter>Thomas Schlechte</submitter>
    <author>Thomas Schlechte</author>
    <author>Christof Schulz</author>
    <author>Ralf Borndörfer</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schlechte">Schlechte, Thomas</collection>
    <collection role="persons" number="schulz">Schulz, Christof</collection>
    <collection role="projects" number="WS-OPT">WS-OPT</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
  </doc>
  <doc>
    <id>9204</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>3:1</pageFirst>
    <pageLast>3:6</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>115</volume>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
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    <title language="eng">Convergence Properties of Newton’s Method for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">The algorithmic efficiency of Newton-based methods for Free Flight Trajectory Optimization is heavily influenced by the size of the domain of convergence. We provide numerical evidence that the convergence radius is much larger in practice than what the theoretical worst case bounds suggest. The algorithm can be further improved by a convergence-enhancing domain decomposition.</abstract>
    <parentTitle language="eng">23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2023.3</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2023-08-27</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-91309</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
  </doc>
  <doc>
    <id>9184</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted>2023</thesisYearAccepted>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>4</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Newton's Method for Global Free Flight Trajectory Optimization</title>
    <abstract language="eng">Globally optimal free flight trajectory optimization can be achieved with a combination of discrete and continuous optimization. A key requirement is that Newton's method for continuous optimization converges in a sufficiently large neighborhood around a minimizer. We show in this paper that, under certain assumptions, this is the case.</abstract>
    <parentTitle language="eng">Operations Research Forum</parentTitle>
    <identifier type="doi">10.1007/s43069-023-00238-z</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-91846</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-89876</enrichment>
    <enrichment key="SourceTitle">Operations Research Forum 4, 63 (2023).</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Fabian Danecker</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="projects" number="MathPlus-TrU-4">MathPlus-TrU-4</collection>
  </doc>
  <doc>
    <id>8325</id>
    <completedYear/>
    <publishedYear>2021</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>27:1</pageFirst>
    <pageLast>27:14</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>207</volume>
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    <publisherName>Schloss Dagstuhl - Leibniz-Zentrum für Informatik</publisherName>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Connected k-partition of k-connected graphs and c-claw-free graphs</title>
    <abstract language="eng">A connected partition is a partition of the vertices of a graph into sets that induce connected subgraphs. Such partitions naturally occur in many application areas such as road networks, and image processing. In these settings, it is often desirable to partition into a fixed number of parts of roughly of the same size or weight. The resulting computational problem is called Balanced Connected Partition (BCP). The two classical objectives for BCP are to maximize the weight of the smallest, or minimize the weight of the largest component. We study BCP on c-claw-free graphs, the class of graphs that do not have K_{1,c} as an induced subgraph, and present efficient (c −1)-approximation algorithms for both objectives. In particular, for 3-claw-free graphs, also simply known as claw-free graphs, we obtain a 2-approximation. Due to the claw-freeness of line graphs, this also implies a 2-approximation for the edge-partition version of BCP in general graphs.&#13;
A harder connected partition problem arises from demanding a connected partition into k parts that have (possibly) heterogeneous target weights w_1, ..., w_k. In the 1970s Győri and Lovász showed that if G is k-connected and the target weights sum to the total size of G, such a partition exists. However, to this day no polynomial algorithm to compute such partitions exists for k &gt; 4. Towards finding such a partition T_1, ..., T_k in k-connected graphs for general k, we show how to efficiently compute connected partitions that at least approximately meet the target weights, subject to the mild assumption that each w_i is greater than the weight of the heaviest vertex. In particular, we give a 3-approximation for both the lower and the upper bounded version i.e. we guarantee that each T_i has weight at least w_i/3 or that each T_i has weight most 3w_i, respectively. Also, we present a both-side bounded version that produces a connected partition where each T_i has size at least w_i/3 and at most max({r, 3})w_i, where r ≥1 is the ratio between the largest and smallest value in w_1, ..., w_k. In particular for the balanced version, i.e. w_1 = w_2 = ... = w_k, this gives a partition with 1/3 w_i ≤ w(T_i) ≤ 3w_i.</abstract>
    <parentTitle language="eng">Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2021</parentTitle>
    <identifier type="doi">10.4230/LIPIcs.APPROX/RANDOM.2021.27</identifier>
    <identifier type="urn">urn:nbn:de:0030-drops-147200</identifier>
    <enrichment key="Series">LIPIcs</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Stephan Schwartz</submitter>
    <author>Katrin Casel</author>
    <author>Davis Issac</author>
    <author>Aikaterini Niklanovits</author>
    <author>Stephan Schwartz</author>
    <author>Ziena Zeif</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schwartz">Schwartz, Stephan</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
  </doc>
  <doc>
    <id>8815</id>
    <completedYear/>
    <publishedYear>2023</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>253</pageFirst>
    <pageLast>277</pageLast>
    <pageNumber/>
    <edition/>
    <issue>2</issue>
    <volume>81</volume>
    <type>article</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2022-11-10</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Vertex Covering with Capacitated Trees</title>
    <abstract language="eng">The covering of a graph with (possibly disjoint) connected subgraphs is a funda-mental problem in graph theory. In this paper, we study a version to cover a graph’svertices by connected subgraphs subject to lower and upper weight bounds, and pro-pose a column generation approach to dynamically generate feasible and promisingsubgraphs. Our focus is on the solution of the pricing problem which turns out to bea variant of the NP-hard Maximum Weight Connected Subgraph Problem. We com-pare different formulations to handle connectivity, and find that a single-commodityflow formulation performs best. This is notable since the respective literature seemsto have widely dismissed this formulation. We improve it to a new coarse-to-fine flowformulation that is theoretically and computationally superior, especially for largeinstances with many vertices of degree 2 like highway networks, where it provides aspeed-up factor of 5 over the non-flow-based formulations. We also propose a pre-processing method that exploits a median property of weight-constrained subgraphs,a primal heuristic, and a local search heuristic. In an extensive computational studywe evaluate the presented connectivity formulations on different classes of instances,and demonstrate the effectiveness of the proposed enhancements. Their speed-upsessentially multiply to an overall factor of well over 10. Overall, our approach allowsthe reliable solution of instances with several hundreds of vertices in a few min-utes. These findings are further corroborated in a comparison to existing districtingmodels on a set of test instances from the literature</abstract>
    <parentTitle language="eng">Networks</parentTitle>
    <identifier type="doi">10.1002/net.22130</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-10-24</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-82616</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Stephan Schwartz</submitter>
    <author>Stephan Schwartz</author>
    <author>William Surau</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schwartz">Schwartz, Stephan</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="persons" number="surau">Surau, William</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
  </doc>
  <doc>
    <id>8881</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>1</pageFirst>
    <pageLast>13</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>106</volume>
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    <publisherName/>
    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Discrete-Continuous Algorithm for Globally Optimal Free Flight Trajectory Optimization</title>
    <abstract language="eng">We present an efficient algorithm that finds a globally optimal solution to the 2D Free Flight Trajectory Optimization Problem (aka Zermelo Navigation Problem) up to arbitrary precision in finite time. The algorithm combines a discrete and a continuous optimization phase. In the discrete phase, a set of candidate paths that densely covers the trajectory space is created on a directed auxiliary graph. Then Yen’s algorithm provides a promising set of discrete candidate paths which subsequently undergo a locally convergent refinement stage. Provided that the auxiliary graph is sufficiently dense, the method finds a path that lies within the convex domain around the global minimizer. From this starting point, the second stage will converge rapidly to the optimum. The density of the auxiliary graph depends solely on the wind field, and not on the accuracy of the&#13;
solution, such that the method inherits the superior asymptotic convergence properties of the optimal control stage.</abstract>
    <parentTitle language="eng">22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2022.2</identifier>
    <enrichment key="Series">Open Access Series in Informatics (OASIcs)</enrichment>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="AcceptedDate">2022-08-01</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Fabian Danecker</author>
    <author>Martin Weiser</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
  </doc>
  <doc>
    <id>8783</id>
    <completedYear/>
    <publishedYear>2022</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>63</pageFirst>
    <pageLast>68</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>conferenceobject</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Rooted Maximum Weight Connected Subgraphs with Balancing and Capacity Constraints</title>
    <abstract language="eng">Finding connected subgraphs of maximum weight subject to additional constraints on the subgraphs is a common (sub)problem in many applications. In this paper, we study the Maximum Weight Connected Subgraph Problem with a given root node and a lower and upper capacity constraint on the chosen subgraph. In addition, the nodes of the input graph are colored blue and red, and the chosen subgraph is required to be balanced regarding its cumulated blue and red weight. This problem arises as an essential subproblem in district planning applications. We show that the problem is NP-hard and give an integer programming formulation. By exploiting the capacity and balancing condition, we develop a powerful reduction technique that is able to significantly shrink the problem size. In addition, we propose a method to strengthen the LP relaxation of our formulation by identifying conflict pairs, i.e., nodes that cannot be both part of a chosen subgraph. Our computational study confirms the positive impact of the new preprocessing technique and of the proposed conflict cuts.</abstract>
    <parentTitle language="eng">Proceedings of the 10th International Network Optimization Conference (INOC), Aachen, Germany, June 7–10, 2022</parentTitle>
    <identifier type="doi">10.48786/inoc.2022.12</identifier>
    <enrichment key="PeerReviewed">yes</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <enrichment key="PreprintUrn">urn:nbn:de:0297-zib-84427</enrichment>
    <submitter>Stephan Schwartz</submitter>
    <author>Ralf Borndörfer</author>
    <author>Stephan Schwartz</author>
    <author>William Surau</author>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="schwartz">Schwartz, Stephan</collection>
    <collection role="projects" number="TOLLCONTROLOPT">TOLLCONTROLOPT</collection>
    <collection role="persons" number="surau">Surau, William</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
  </doc>
  <doc>
    <id>8419</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>2021-09-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Optimal Line Plans in the Parametric City and the Impact of In-Motion Costs</title>
    <abstract language="eng">Line planning in public transport involves determining vehicle routes and assigning frequencies of service such that travel demands are satisfied. We evaluate how line plans, which are optimal with respect to in-motion costs (IMC), the objective function depending purely on arc-lengths for both user and operator costs, performs with respect to the value of resources consumed (VRC). The latter is an elaborate, socio-economic cost function which includes discomfort caused by delay, boarding and alighting times, and transfers. Even though discomfort is a large contributing factor to VRC and is entirely disregarded in IMC, we observe that the two cost functions are qualitatively comparable.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-84195</identifier>
    <enrichment key="opus.source">publish</enrichment>
    <author>Berenike Masing</author>
    <submitter>Berenike Masing</submitter>
    <author>Niels Lindner</author>
    <author>Ralf Borndörfer</author>
    <series>
      <title>ZIB-Report</title>
      <number>21-27</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>line planning</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>public transport</value>
    </subject>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>mixed-integer prgramming</value>
    </subject>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="lindner">Lindner, Niels</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="persons" number="masing">Masing, Berenike</collection>
    <collection role="projects" number="SymLPP">SymLPP</collection>
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  <doc>
    <id>9773</id>
    <completedYear/>
    <publishedYear>2024</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst>13:1</pageFirst>
    <pageLast>13:19</pageLast>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume>123</volume>
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    <publisherPlace/>
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    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2024-10-07</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">A Bayesian Rolling Horizon Approach for Rolling Stock Rotation Planning with Predictive Maintenance</title>
    <abstract language="eng">We consider the rolling stock rotation planning problem with predictive maintenance (RSRP-PdM), where a timetable given by a set of trips must be operated by a fleet of vehicles. Here, the health states of the vehicles are assumed to be random variables, and their maintenance schedule should be planned based on their predicted failure probabilities. Utilizing the Bayesian update step of the Kalman filter, we develop a rolling horizon approach for RSRP-PdM, in which the predicted health state distributions are updated as new data become available. This approach reduces the uncertainty of the health states and thus improves the decision-making basis for maintenance planning. To solve the instances, we employ a local neighborhood search, which is a modification of a heuristic for RSRP-PdM, and demonstrate its effectiveness. Using this solution algorithm, the presented approach is compared with the results of common maintenance strategies on test instances derived from real-world timetables. The obtained results show the benefits of the rolling horizon approach.</abstract>
    <parentTitle language="eng">24th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2024)</parentTitle>
    <identifier type="doi">10.4230/OASIcs.ATMOS.2024.13</identifier>
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    <enrichment key="PeerReviewed">yes</enrichment>
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    <author>Felix Prause</author>
    <submitter>Felix Prause</submitter>
    <author>Ralf Borndörfer</author>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="projects" number="MODAL-Gesamt">MODAL-Gesamt</collection>
    <collection role="persons" number="prause">Prause, Felix</collection>
    <collection role="institutes" number="ais2t">AI in Society, Science, and Technology</collection>
    <collection role="institutes" number="neo">Network Optimization</collection>
    <collection role="projects" number="MODAL-MobilityLab">MODAL-MobilityLab</collection>
    <collection role="projects" number="BerDiBa">BerDiBa</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
  </doc>
  <doc>
    <id>10308</id>
    <completedYear/>
    <publishedYear>2026</publishedYear>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
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    <type>conferenceobject</type>
    <publisherName/>
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    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>--</completedDate>
    <publishedDate>--</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">An Eikonal Approach for Globally Optimal Free Flight Trajectories</title>
    <abstract language="eng">We present an eikonal-based approach that is capable of finding a continuous globally optimal trajectory for an aircraft in a stationary wind field. This minimizes emissions and fuel consumption. If the destination is close to a cut locus of the associated Hamilton-Jacobi-Bellman equation, small numerical discretization errors can lead to selecting a merely locally optimal trajectory and missing the globally optimal one. Based on finite element error estimates, we construct a trust region around the cut loci in order to guarantee uniqueness of trajectories for destinations sufficiently far from cut loci.</abstract>
    <identifier type="arxiv">2603.11830</identifier>
    <enrichment key="PeerReviewed">no</enrichment>
    <enrichment key="SubmissionStatus">under review</enrichment>
    <enrichment key="opus.source">publish</enrichment>
    <author>Ralf Borndörfer</author>
    <submitter>Martin Weiser</submitter>
    <author>Arturas Jocas</author>
    <author>Martin Weiser</author>
    <collection role="institutes" number="num">Numerical Mathematics</collection>
    <collection role="persons" number="borndoerfer">Borndörfer, Ralf</collection>
    <collection role="persons" number="weiser">Weiser, Martin</collection>
    <collection role="institutes" number="MSoCP">Modeling and Simulation of Complex Processes</collection>
    <collection role="projects" number="MathPlus-AA3-3">MathPlus-AA3-3</collection>
    <collection role="persons" number="jocas">Jocas, Arturas</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
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