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The Transport PDE and Mixed-Integer Linear Programming

Authors: Armin Fügenschuh, Björn Geißler, Alexander Martin, and Antonio Morsi

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract

Discrete, nonlinear and PDE constrained optimization are mostly considered as different fields of mathematical research. Nevertheless many real-life problems are most naturally modeled as PDE constrained mixed integer nonlinear programs. For example, nonlinear network flow problems where the flow dynamics are governed by a transport equation are of this type. We present four different applications together with the derivation of the associated transport equations and we show how to model these problems in terms of mixed integer linear constraints.

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Armin Fügenschuh, Björn Geißler, Alexander Martin, and Antonio Morsi. The Transport PDE and Mixed-Integer Linear Programming. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{fugenschuh_et_al:DagSemProc.09261.31,
  author =	{F\"{u}genschuh, Armin and Gei{\ss}ler, Bj\"{o}rn and Martin, Alexander and Morsi, Antonio},
  title =	{{The Transport PDE and Mixed-Integer Linear Programming}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--9},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.31},
  URN =		{urn:nbn:de:0030-drops-21679},
  doi =		{10.4230/DagSemProc.09261.31},
  annote =	{Keywords: Transport Equation, Partial Differential Equation, Mixed-Integer Linear Programming, Modeling, Nonlinear Constraints}
}

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DOI: 10.4230/OASIcs.ATMOS.2006.686

Locomotive and Wagon Scheduling in Freight Transport

Authors: Armin Fügenschuh, Henning Homfeld, Andreas Huck, and Alexander Martin

Published in: OASIcs, Volume 5, 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06) (2006)

Abstract

We present a new model for a strategic locomotive scheduling problem arising at the Deutsche Bahn AG. The model is based on a multi-commodity min-cost flow formulation that is also used for public bus scheduling problems. However, several new aspects have to be additionally taken into account, such as cyclic departures of the trains, time windows on starting and arrival times, network-load dependend travel times, and a transfer of wagons between trains. The model is formulated as an integer programming problem, and solutions are obtained using commercial standard software. Computational results for several test instances are presented.

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Armin Fügenschuh, Henning Homfeld, Andreas Huck, and Alexander Martin. Locomotive and Wagon Scheduling in Freight Transport. In 6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06). Open Access Series in Informatics (OASIcs), Volume 5, pp. 1-14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{fugenschuh_et_al:OASIcs.ATMOS.2006.686,
  author =	{F\"{u}genschuh, Armin and Homfeld, Henning and Huck, Andreas and Martin, Alexander},
  title =	{{Locomotive and Wagon Scheduling in Freight Transport}},
  booktitle =	{6th Workshop on Algorithmic Methods and Models for Optimization of Railways (ATMOS'06)},
  pages =	{1--14},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-01-9},
  ISSN =	{2190-6807},
  year =	{2006},
  volume =	{5},
  editor =	{Jacob, Riko and M\"{u}ller-Hannemann, Matthias},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.ATMOS.2006.686},
  URN =		{urn:nbn:de:0030-drops-6863},
  doi =		{10.4230/OASIcs.ATMOS.2006.686},
  annote =	{Keywords: Freight Transport, Vehicle Scheduling, Time Windows, Integer Programming.}
}

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Documents authored by Martin, Alexander

The Transport PDE and Mixed-Integer Linear Programming

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Locomotive and Wagon Scheduling in Freight Transport

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