A Mass Transportation Model for the Optimal Planning of an Urban Region

TL;DR

This paper introduces a mass transportation model for optimal urban planning, balancing transportation costs with penalties for resident concentration and service dispersion, using advanced mathematical theories.

Contribution

It develops a novel model combining Monge--Kantorovich transportation theory with nonconvex measure functionals for urban planning optimization.

Findings

Effective framework for balancing transportation and distribution costs.

Mathematical foundation for urban distribution optimization.

Potential applications in city planning and resource allocation.

Abstract

We propose a model to describe the optimal distributions of residents and services in a prescribed urban area. The cost functional takes into account the transportation costs (according to a Monge--Kantorovich-type criterion) and two additional terms which penalize concentration of residents and dispersion of services. The tools we use are the Monge--Kantorovich mass transportation theory and the theory of nonconvex functionals defined on measures.