Optimal networks for mass transportation problems

¹ Alessio Brancolini, Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy; a.brancolini@sns.it
² Giuseppe Buttazzo, Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy; buttazzo@dm.unipi.it

Received: 21 October 2003

Abstract

In the framework of transport theory, we are interested in the following optimization problem: given the distributions µ⁺ of working people and µ^- of their working places in an urban area, build a transportation network (such as a railway or an underground system) which minimizes a functional depending on the geometry of the network through a particular cost function. The functional is defined as the Wasserstein distance of µ⁺ from µ^- with respect to a metric which depends on the transportation network.