Calculus of Variations and Geometric Measure Theory

G. Buttazzo - S. Guarino Lo Bianco - F. Oliviero

Optimal location problems with routing cost

created by buttazzo on 25 Jun 2013


Accepted Paper

Inserted: 25 jun 2013
Last Updated: 25 jun 2013

Journal: Discrete Contin. Dyn. Syst.
Year: 2013

2010 Mathematics Subject Classification: 49Q10, 49Q20, 90B80, 90B85


In the paper a model problem for the location of a given number $N$ of points in a given region $\Omega$ and with a given resources density $\rho(x)$ is considered. The main difference between the usual location problems and the present one is that in addition to the location cost an extra {\it routing cost} is considered, that takes into account the fact that the resources have to travel between the locations on a point-to-point basis. The limit problem as $N\to\infty$ is characterized and some applications to airfreight systems are shown.

Keywords: Gamma-convergence, transport problems, location problems, routing costs