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Single-Facility Location Problems with Barriers

  • Textbook
  • © 2002

Overview

Authors:
  1. Kathrin Klamroth

    1. Institute of Applied Mathematics, University of Erlange-Nuremberg, Erlangen, Germany

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction and General Results

    1. Front Matter

      Pages 1-1
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    2. Measuring Distances

      • Kathrin Klamroth
      Pages 3-14

    3. Shortest Paths in the Presence of Barriers

      • Kathrin Klamroth
      Pages 15-38

    4. Location Problems with Barriers: Basic Concepts and Literature Review

      • Kathrin Klamroth
      Pages 39-48

    5. Bounds for Location Problems with Barriers

      • Kathrin Klamroth
      Pages 49-54

  3. Solution Methods for Specially Shaped Barriers

    1. Front Matter

      Pages 55-55
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    2. Planar Location Problems with Polyhedral Barriers

      • Kathrin Klamroth
      Pages 57-83

    3. Location Problems with a Circular Barrier

      • Kathrin Klamroth
      Pages 85-99

    4. Weber Problems with a Line Barrier

      • Kathrin Klamroth
      Pages 101-117

  4. Solution Methods for Special Distance and Objective Functions

    1. Front Matter

      Pages 119-119
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    2. Weber Problems with Block Norms

      • Kathrin Klamroth
      Pages 121-133

    3. Center Problems with the Manhattan Metric

      • Kathrin Klamroth
      Pages 135-151

    4. Multicriteria Location Problems with Polyhedral Barriers

      • Kathrin Klamroth
      Pages 153-169

  5. Application

    1. Front Matter

      Pages 171-171
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    2. Location with Barriers Put to Work in Practice

      • Kathrin Klamroth
      Pages 173-182

  6. Back Matter

    Pages 183-201
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Keywords

About this book

Everyday life bears a multitude of location problems and locational de- sions. These may be as simple as how best to place a pencil on a desk without having to reach too far and still keeping the work space clear, up to the question of where to place the next out of hundreds of thousands of transistors on a microchip. Some of these questions have easy answers, while others are so complex that not even satisfactory solutions are ava- able, never mind asking for optimized placement. The scales of problems reach from microchip design up to global trade and may demand consid- ation of one, two, three, or even more dimensions. As modern life encounters an ever increasing concentration in many - spects, usually a multitude of restrictions will be imposed on a problem. Theserestrictionsmaybeclassi?edasregionsoflimitedorforbiddenpla- ment of a new facility or as regions with limitations on traveling. Areas where the placement of a new facility is forbidden, referred to as forbidden regions,canbeusedtomodel,forexample,protectedareasorregionswhere thegeographiccharacteristicsforbidtheconstructionofthedesiredfacility. Limitations on traveling are constituted by barrier regions or obstacles like military regions,mountainranges,lakes,big rivers,interstatehighways,or, on smaller scales, machinery and conveyor belts in an industrial plant.

Authors and Affiliations

  • Institute of Applied Mathematics, University of Erlange-Nuremberg, Erlangen, Germany

    Kathrin Klamroth

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