Calculus of Variations and Geometric Measure Theory

G. Buttazzo - F. Santambrogio - E. Stepanov

Asymptotic optimal location of facilities in a competition between population and industries

created by stepanov on 22 Mar 2011
modified on 11 Oct 2014


Published Paper

Inserted: 22 mar 2011
Last Updated: 11 oct 2014

Journal: Ann. Scuola Norm. Sup. Pisa Cl. Sci.
Volume: 12
Number: 1
Pages: 239–273
Year: 2013


We consider the problem of optimally locating a given number $k$ of industrial facilities (modeled by points in $*R*^n$) for an integral cost function which takes into account two measures $\varphi^+$ and $\varphi^-$, which represent the parts of a populations that respectively wants to be as close as possible (e.g.\ industries) and as far as possible (e.g.\ private citizens) to the facilities. The asymptotic analysis as $k\to\infty$ is performed, providing the asymptotic density of optimal locations.

Keywords: optimal transportation, average distance functional, location problem, facility location, Fermat-Weber problem, k-median problem