*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

**Abstract:**

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

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