Optimal location problems with routing cost

Giuseppe Buttazzo; Serena Guarino Lo Bianco; Fabrizio Oliviero

doi:10.3934/dcds.2014.34.1301

Article Contents

2014, Volume 34, Issue 4: 1301-1317. Doi: 10.3934/dcds.2014.34.1301

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Optimal location problems with routing cost

1.
Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa
2.
Dipartimento di Matematica - Università di Pisa, Largo B. Pontecorvo, 5, 56127 Pisa
3.
Dipartimento di Ingegneria Aerospaziale - Università di Pisa, Via G. Caruso, 8, 56122 Pisa

Received: July 31, 2012

Revised: October 31, 2012

Published: March 2014

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Abstract

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 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.

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Mathematics Subject Classification: Primary: 49Q10, 49Q20; Secondary: 90B80, 90B85.

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