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Numerical solutions of the mass transfer problem

Published online by Cambridge University Press:  01 July 2006

Serge Dubuc  and
Issa Kagabo
Serge Dubuc
Affiliation:
Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada; [email protected]
Issa Kagabo
Affiliation:
Department of Mathematics, Columbia Union College, 7600 Flower Avenue, Takoma Park, MD, 20912, USA; [email protected]
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Abstract

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 ∫∫ c(x,y)dξ(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.

Keywords

Continuous programmingtransportationmass transferoptimization.
Type
Research Article
Information
RAIRO - Operations Research , Volume 40 , Issue 1 , January 2006 , pp. 1 - 17
Copyright
© EDP Sciences, 2006

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