Some generalizations of the circular city model

This paper contains two generalizations of a previous model studied by Zitron which dealt with a continuous approach to the determination of minimal cost transportation routes. That model consisted of a circular central business district where the cost density of construction is constant surrounded...

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Bibliographic Details
Published in:Mathematical modelling 1980, Vol.1 (2), p.167-179
Main Authors: Brakke, K.A., Zitron, N.R.
Format: Article
Language:English
Subjects:
calculus of variations
economic planning
modelling
Operations research
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Summary:This paper contains two generalizations of a previous model studied by Zitron which dealt with a continuous approach to the determination of minimal cost transportation routes. That model consisted of a circular central business district where the cost density of construction is constant surrounded by an annular transition region whose cost density varies inversely as the distance from the center. The region surrounding the annular transition region has constant cost density. In the previous case, an analysis was carried out which permitted the determination of minimal-cost routes between two diametrically opposite points at the city limits. The present paper generalizes these results to the case where the origin and destination are at the city limits but need not be diametrically opposite and to the case where the points are diametrically opposite but lie outside the city limits.
ISSN:0270-0255
1878-7231
DOI:10.1016/0270-0255(80)90035-4