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Numerical solutions of the mass transfer problem

Serge Dubuc;  Issa Kagabo — 2006

RAIRO - Operations Research

Let and be two probability measures on the real line and let be a lower semicontinuous function on the plane. The mass transfer problem consists in determining a measure whose marginals coincide with and , and whose total cost d 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 . We illustrate these numerical methods and determine the convergence...

Trivial Cases for the Kantorovitch Problem

Serge Dubuc;  Issa Kagabo;  Patrice Marcotte — 2010

RAIRO - Operations Research

Let and be two compact spaces endowed with respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on whose marginals coincide with and , and such that the total cost be minimized. We first show that if the cost function is decomposable, i.e., can be represented as the sum of two continuous functions defined on and , respectively, then every feasible measure is optimal. Conversely, when...

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