Numerical solutions of the mass transfer problem

Issue		RAIRO Oper. Res. Volume 40, Number 1, January-March 2006


Page(s)		1 - 17
DOI		10.1051/ro:2006011
Published online		01 July 2006

RAIRO Oper. Res. 40 (2006) 1-17
DOI: 10.1051/ro:2006011

Numerical solutions of the mass transfer problem

Serge Dubuc¹ and Issa Kagabo²

¹ Département de mathématiques et de statistique, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, H3C 3J7, Canada; dubucs@dms.umontreal.ca
² Department of Mathematics, Columbia Union College, 7600 Flower Avenue, Takoma Park, MD, 20912, USA; ikagabo@cuc.edu

(Received December 10, 2003. Accepted November 7, 2005. / Published online: 1 July 2006)

Abstract
Let $\mu$ and $\nu$ 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 $\xi$ whose marginals coincide with $\mu$ and $\nu$ , and whose total cost $\iint\,\,c(x,y)\,{\rm d}\xi(x,y)$ 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.

Key words: Continuous programming, transportation, mass transfer, optimization.

© EDP Sciences 2006

What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.

If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.