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Solving Network Design Problems via Decomposition, Aggregation and Approximation

  • Book
  • © 2016

Overview

Authors:
  1. Andreas Bärmann

    1. Dept. Mathe/Lehrstu. f. Wirtschaftsmathe, FAU Erlangen-Nürnberg, Erlangen, Germany

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  • A Study in the Field of Mathematics

  • Includes supplementary material: sn.pub/extras

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XV
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  2. Introduction

    • Andreas Bärmann
    Pages 1-5

  3. Decomposition Algorithms for Multi-Period Network Design

    1. Front Matter

      Pages 7-9
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    2. Motivation

      • Andreas Bärmann
      Pages 11-14

    3. Strategic Infrastructure Planning in Railway Networks

      • Andreas Bärmann
      Pages 15-47

    4. Modelling the Expansion Problem

      • Andreas Bärmann
      Pages 49-66

    5. Model Analysis and Solution Approaches

      • Andreas Bärmann
      Pages 67-84

    6. Case Study for the German Railway Network

      • Andreas Bärmann
      Pages 85-102

  4. Iterative Aggregation Procedures for Network Design Problems

    1. Front Matter

      Pages 103-105
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    2. Motivation

      • Andreas Bärmann
      Pages 107-109

    3. An Iterative Aggregation Algorithm for Optimal Network Design

      • Andreas Bärmann
      Pages 111-121

    4. Integration of Routing Costs into the Aggregation Scheme

      • Andreas Bärmann
      Pages 123-134

    5. The Computational Impact of Aggregation

      • Andreas Bärmann
      Pages 135-153

  5. Approximate Second-Order Cone Robust Optimization

    1. Front Matter

      Pages 155-156
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    2. Motivation

      • Andreas Bärmann
      Pages 159-162

    3. Polyhedral Approximation of Second-Order Cone Robust Counterparts

      • Andreas Bärmann
      Pages 163-177

    4. Computational Assessment of Approximate Robust Optimization

      • Andreas Bärmann
      Pages 179-188

    5. Conclusions and Outlook

      • Andreas Bärmann
      Pages 189-191

  6. Back Matter

    Pages 193-203
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Keywords

About this book

Andreas Bärmann develops novel approaches for the solution of network design problems as they arise in various contexts of applied optimization. At the example of an optimal expansion of the German railway network until 2030, the author derives a tailor-made decomposition technique for multi-period network design problems. Next, he develops a general framework for the solution of network design problems via aggregation of the underlying graph structure. This approach is shown to save much computation time as compared to standard techniques. Finally, the author devises a modelling framework for the approximation of the robust counterpart under ellipsoidal uncertainty, an often-studied case in the literature. Each of these three approaches opens up a fascinating branch of research which promises a better theoretical understanding of the problem and an increasing range of solvable application settings at the same time.

Authors and Affiliations

  • Dept. Mathe/Lehrstu. f. Wirtschaftsmathe, FAU Erlangen-Nürnberg, Erlangen, Germany

    Andreas Bärmann

About the author

Dr. Andreas Bärmann is currently working as a postdoctoral researcher at the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) at the chair of Economics, Discrete Optimization and Mathematics. His research is focussed on mathematical optimization, especially the optimization of logistic processes.

Bibliographic Information

  • Book Title: Solving Network Design Problems via Decomposition, Aggregation and Approximation

  • Authors: Andreas Bärmann

  • DOI: https://doi.org/10.1007/978-3-658-13913-1

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2016

  • Softcover ISBN: 978-3-658-13912-4Published: 10 June 2016

  • eBook ISBN: 978-3-658-13913-1Published: 02 June 2016

  • Edition Number: 1

  • Number of Pages: XV, 203

  • Number of Illustrations: 4 b/w illustrations, 28 illustrations in colour

  • Topics: Optimization, Operations Research/Decision Theory, Logistics

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