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...
Given the probability measure over the given region , we consider the optimal location of a set composed by points in in order to minimize the average distance (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...
Given the probability measure over the given region
, we consider the optimal location of a set
composed by points in in order to minimize the
average distance (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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