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Given the probability measure $\nu$ over the given region $\Omega\subset\R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$points $\Om$ in order to minimize the average distance $\Sigma\mapsto \int_\Om\dist(x,\Sigma) d\nu$ (the classical optimal facility location problem). Thepaper compares two strategies to find optimal configurations: the long-term onewhich consists in placing all $n$ points at once in an optimal position, andthe short-term one which consists in placing the points one by one adding ateach step at most one point and preserving the configuration built at previoussteps. We show that the respective optimization problems exhibit qualitativelydifferent asymptotic behavior as $n\to\infty$, although the optimization costsin both cases have the same asymptotic orders of vanishing.

Optimal networks for mass transportation problems