Entropy maximization models in regional and urban planning

Abstract

The Entropy‐Maximization Principle has been examined from both the statistical‐mechanics and information‐theoretic points of view and has been applied to obtain solutions for some population‐density and transportation models. For the former, the well‐known negative exponential and quadratic gamma distributions have been obtained and the problem of simultaneous determination of population density and rent has been solved. The transportation models considered include production‐constrained model, attraction‐constrained model, production‐attraction‐constrained model, a model for transportation by different modes, and models for transportation via intermediate points. Both continuous and discrete models are considered. In the usual models, entropy is maximized subject to cost of travel being fixed and known. This cost is however not known so the models are conceptually weak. Here a new point of view is given drawing its inspiration from optimal portfolio selection theory and Pareto optimality. An attempt at maximizing the entropy and minimizing the cost is made to obtain a cost‐efficient entropy‐maximizing function. Some interesting results are obtained for both types of models and the existing models are reestablished on a logically sounder foundation.

Notes

†On leave of absence from Indian Institute of Technology, Kanpur, India

Additional information

Notes on contributors

J. N. Kapur†

†On leave of absence from Indian Institute of Technology, Kanpur, India