Article contents
Long-term planning versus short-term planning in the asymptotical location problem
Published online by Cambridge University Press: 30 May 2008
Abstract
Given the probability measure ν over the given region
$\Omega\subset \mathbb{R}^n$, we consider the optimal location of a set
Σ composed by n points in Ω in order to minimize the
average distance $\Sigma\mapsto \int_\Omega \mathrm{dist}\,(x,\Sigma)\,{\rm d}\nu$
(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 the configuration
built at previous steps. We show that the respective optimization
problems exhibit qualitatively different asymptotic behavior as
$n\to\infty$
, although the optimization costs in both cases have the same asymptotic
orders of vanishing.
Keywords
- Type
- Research Article
- Information
- ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 3 , July 2009 , pp. 509 - 524
- Copyright
- © EDP Sciences, SMAI, 2008
References
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