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    <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>
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    <identifier type="urn">urn:nbn:de:0297-zib-73868</identifier>
    <identifier type="doi">https://doi.org/https://doi.org/10.1007/978-3-030-48439-2_92</identifier>
    <author>Fabian Löbel</author>
    <submitter>Niels Lindner</submitter>
    <author>Niels Lindner</author>
    <author>Ralf Borndörfer</author>
    <series>
      <title>ZIB-Report</title>
      <number>19-36</number>
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    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Periodic Event Scheduling Problem</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Periodic Timetabling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Integrated Passenger Routing</value>
    </subject>
    <subject>
      <language>eng</language>
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      <value>Shortest Routes in Public Transport</value>
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    <title language="eng">Non-linear Battery Behavior in Electric Vehicle Scheduling Problems</title>
    <abstract language="eng">The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.</abstract>
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    <enrichment key="ConferencePlace">Hamburg, Germany</enrichment>
    <enrichment key="ConferenceTitle">International Conference on Operations Research (OR 2023)</enrichment>
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    <author>Fabian Löbel</author>
    <editor>Guido Voigt</editor>
    <submitter>Fabian Löbel</submitter>
    <author>Ralf Borndörfer</author>
    <editor>Malte Fliedner</editor>
    <author>Steffen Weider</author>
    <editor>Knut Haase</editor>
    <editor>Wolfgang Brüggermann</editor>
    <editor>Kai Hoberg</editor>
    <editor>Joern Meissner</editor>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Electric Vehicle Scheduling</value>
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      <language>eng</language>
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    <title language="eng">The Modulo Network Simplex with Integrated Passenger Routing</title>
    <abstract language="eng">Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration.</abstract>
    <parentTitle language="eng">Operations Research Proceedings 2016</parentTitle>
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    <author>Ralf Borndörfer</author>
    <submitter>Heide Hoppmann</submitter>
    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <author>Fabian Löbel</author>
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    <publishedDate>2016-08-29</publishedDate>
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    <title language="eng">The Modulo Network Simplex with Integrated Passenger Routing</title>
    <abstract language="eng">Periodic timetabling is an important strategic planning problem in public transport. The task is to determine periodic arrival and departure times of the lines in a given network, minimizing the travel time of the passengers. We extend the modulo network simplex method, a well-established heuristic for the periodic timetabling problem, by integrating a passenger (re)routing step into the pivot operations. Computations on real-world networks show that we can indeed find timetables with much shorter total travel time, when we take the passengers' travel paths into consideration.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-60319</identifier>
    <enrichment key="SourceTitle">To appear in: Operations Research Proceedings 2016</enrichment>
    <author>Ralf Borndörfer</author>
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    <author>Heide Hoppmann</author>
    <author>Marika Karbstein</author>
    <author>Fabian Löbel</author>
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      <title>ZIB-Report</title>
      <number>16-43</number>
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      <language>eng</language>
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      <value>periodic timetabling, modulo network simplex, passenger routing</value>
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    <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>
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    <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>
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    <enrichment key="AcceptedDate">2024-08-07</enrichment>
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    <submitter>Fabian Löbel</submitter>
    <author>Ralf Borndörfer</author>
    <author>Andreas Löbel</author>
    <author>Fabian Löbel</author>
    <author>Steffen Weider</author>
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    <title language="eng">Non-Linear Battery Behavior in Electric Vehicle Scheduling Problems</title>
    <abstract language="eng">The currently most popular approach to handle non-linear battery behavior for electric vehicle scheduling is to use a linear spline interpolation of the charge curve. We show that this can lead to approximate models that underestimate the charge duration and overestimate the state of charge, which is not desirable. While the error is of second order with respect to the interpolation step size, the associated mixed-integer linear programs do not scale well with the number of spline segments. It is therefore recommendable to use coarse interpolation grids adapted to the curvature of the charge curve, and to include sufficient safety margins to ensure solutions of approximate models remain feasible subjected to the exact charge curve.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-92441</identifier>
    <identifier type="doi">10.1007/978-3-031-58405-3_53</identifier>
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    <author>Fabian Löbel</author>
    <submitter>Fabian Löbel</submitter>
    <author>Ralf Borndörfer</author>
    <author>Steffen Weider</author>
    <series>
      <title>ZIB-Report</title>
      <number>23-24</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Electric Vehicle Scheduling</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>Non-Linear Charging</value>
    </subject>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
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    <title language="eng">Non-Linear Charge Functions for Electric Vehicle Scheduling with Dynamic Recharge Rates</title>
    <abstract language="eng">The ongoing electrification of logistics systems and vehicle fleets increases the complexity of associated vehicle routing or scheduling problems.&#13;
Battery-powered vehicles have to be scheduled to recharge in-service, and the relationship between charging time and replenished driving range is non-linear.&#13;
In order to access the powerful toolkit offered by mixed-integer and linear programming techniques, this battery behavior has to be linearized.&#13;
Moreover, as electric fleets grow, power draw peaks have to be avoided to save on electricity costs or to adhere to hard grid capacity limits, such that it becomes desirable to keep recharge rates dynamic.&#13;
We suggest a novel linearization approach of battery charging behavior for vehicle scheduling problems, in which the recharge rates are optimization variables and not model parameters.</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.2023.15</identifier>
    <identifier type="urn">urn:nbn:de:0030-drops-187765</identifier>
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    <enrichment key="AcceptedDate">2023-07-31</enrichment>
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    <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>
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    <publishedYear>2020</publishedYear>
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    <publisherName>Springer International Publishing</publisherName>
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    <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>
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