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Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem

Giuseppe Buttazzo;  Eugene Stepanov — 2003

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In the paper the problem of constructing an optimal urban transportation network in a city with given densities of population and of workplaces is studied. The network is modeled by a closed connected set of assigned length, while the optimality condition consists in minimizing the Monge-Kantorovich functional representing the total transportation cost. The cost of trasporting a unit mass between two points is assumed to be proportional to the distance between them when the transportation is carried...

Long-term planning versus short-term planning in the asymptotical location problem

Alessio Brancolini;  Giuseppe Buttazzo;  Filippo Santambrogio;  Eugene Stepanov — 2009

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure ν over the given region Ω ⊂ ℝ n , we consider the optimal location of a set Σ composed by n points in Ω in order to minimize the average distance Σ ↦ ∫ Ω dist ( x , Σ ) d ν (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all n points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving...

Long-term planning short-term planning in the asymptotical location problem

Alessio Brancolini;  Giuseppe Buttazzo;  Filippo Santambrogio;  Eugene Stepanov — 2008

ESAIM: Control, Optimisation and Calculus of Variations

Given the probability measure over the given region Ω ⊂ ℝ n , we consider the optimal location of a set composed by points in in order to minimize the average distance Σ ↦ ∫ Ω dist ( x , Σ ) d ν (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the...

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