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."
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