Optimal Spatial Interaction and the Gravity Model

1. Front Matter

   Pages N2-vii

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2. The Transportation Planning Process

   1. The Transportation Planning Process

      • Sven Erlander

      Pages 1-13

3. On Entropy

   1. Front Matter

      Pages 15-15

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   2. Entropy as a Measure of Dispersion

      • Sven Erlander

      Pages 17-23

   3. Some Comments Upon Entropy Maximizing

      • Sven Erlander

      Pages 25-26

4. The Doubly Constrained Trip Distribution Problem

   1. Front Matter

      Pages 27-27

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   2. A Model for the Constraints

      • Sven Erlander

      Pages 29-31

   3. The Objective Function and Our Minimization Problem

      • Sven Erlander

      Pages 33-34

   4. The Gravity Model as the Optimal Solution of the Entropy Constrained Aggregate Linear Program

      • Sven Erlander

      Pages 35-53

   5. Sensitivity and the Dual Program

      • Sven Erlander

      Pages 55-63

   6. Interactivity and Entropy

      • Sven Erlander

      Pages 65-67

   7. Benefit Measures and the Gravity Model

      • Sven Erlander

      Pages 69-70

5. Modal Split and Assignment

   1. Front Matter

      Pages 71-71

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   2. Modal Split

      • Sven Erlander

      Pages 73-76

   3. Assignment to the Network

      • Sven Erlander

      Pages 77-78

6. Maximizing Total Utility

   1. Front Matter

      Pages 79-79

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   2. An Utility Approach to the Original Trip Distribution Problem

      • Sven Erlander

      Pages 81-90

   3. Entropy Constrained Aggregate Linear Program

      • Sven Erlander

      Pages 91-95

7. Back Matter

   Pages 97-113

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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

• Department of Mathematics, Linköping Institute of Technology, Linköping, Sweden

  Sven Erlander

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