© 1980

Optimal Spatial Interaction and the Gravity Model

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 173)

Table of contents

  1. Front Matter
    Pages N2-vii
  2. The Transportation Planning Process

    1. Sven Erlander
      Pages 1-13
  3. On Entropy

    1. Front Matter
      Pages 15-15
    2. Sven Erlander
      Pages 17-23
    3. Sven Erlander
      Pages 25-26
  4. The Doubly Constrained Trip Distribution Problem

    1. Front Matter
      Pages 27-27
    2. Sven Erlander
      Pages 29-31
    3. Sven Erlander
      Pages 55-63
    4. Sven Erlander
      Pages 65-67
    5. Sven Erlander
      Pages 69-70
  5. Modal Split and Assignment

    1. Front Matter
      Pages 71-71
    2. Sven Erlander
      Pages 73-76
    3. Sven Erlander
      Pages 77-78
  6. Maximizing Total Utility

    1. Front Matter
      Pages 79-79
  7. Back Matter
    Pages 97-113

About this book


This book has grown out of a desire to explore the possibilities of using optimizing models in transportation planning. This approach has been followed throughout. Models which combine descriptive and optimizing elements are not treated. The gravity model is here studied as the solution to an optimizing model. In spite of this approach, much of the material shoula be of general interest. Algorithms are not discussed. The author has benefited from discussions with many colleagues. M. Florian suggested the term "interacti vi ty". N. F. Stewart and P. Smeds gave many valu­ able comments on a first draft. M. Beckmann made me think once more about the final chapters. R. Grubbstrem and K. Jornsten helped clarifYing some things in the same chapters. Remaining insufficiencies are due to the author. Gun Mannervik typed with great patience. Linkoping in October 1979 Sven Erlander ABSTRACT The book proposes extended use of optimizing models in transportation plann­ ing. An entropy constrained linear program for the trip distribution problem is formulated and shown to have the ordinarJ doubly constrained gravity model as its solution. Entropy is here used as a measure of interactivity, which is constrained to be at a prescribed level. In this way the variation present in the reference trip matrix is preserved. (The properties of entropy as a dispersion measure are shortly discussed. ) The detailed mathematics of the optimal solutions as well as of sensitivity and duality are given.


Gravitationsmodell (Wirtsch.) Gravity Interaction Optimierung Transportproblem algorithms linear optimization

Authors and affiliations

  1. 1.Department of MathematicsLinköping Institute of TechnologyLinköpingSweden

Bibliographic information

  • Book Title Optimal Spatial Interaction and the Gravity Model
  • Authors Sven Svenaeus
  • Series Title Lecture Notes in Economics and Mathematical Systems
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1980
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-09729-7
  • eBook ISBN 978-3-642-45515-5
  • Series ISSN 0075-8442
  • Edition Number 1
  • Number of Pages IX, 113
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Regional/Spatial Science
  • Buy this book on publisher's site
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