Numerical solutions of the mass transfer problem

Dubuc, Serge; Kagabo, Issa

doi:10.1051/ro:2006011

Dubuc, Serge ; Kagabo, Issa

RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 1-17.

Résumé

Let $μ$ and $ν$ be two probability measures on the real line and let $c$ be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure $ξ$ whose marginals coincide with $μ$ and $ν$ , and whose total cost $\int \int c (x, y) d ξ (x, y)$ is minimum. In this paper we present three algorithms to solve numerically this Monge-Kantorovitch problem when the commodity being shipped is one-dimensional and not necessarily confined to a bounded interval. We illustrate these numerical methods and determine the convergence rate.

DOI : 10.1051/ro:2006011

Mots clés : continuous programming, transportation, mass transfer, optimization

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     title = {Numerical solutions of the mass transfer problem},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {1--17},
     publisher = {EDP-Sciences},
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Dubuc, Serge; Kagabo, Issa. Numerical solutions of the mass transfer problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 40 (2006) no. 1, pp. 1-17. doi : 10.1051/ro:2006011. http://www.numdam.org/articles/10.1051/ro:2006011/

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