The paper yields an investigation of the set of all finite measures on the product space with given difference of marginals. Extremal points of this set are characterized and constructed. Sets of uniqueness are studied in the relation to marginal problem. In the optimization problem the support of the optimal measure is described for a class of cost functions. In an example the optimal value is reached by an unbounded sequence of measures.
@article{118475,
author = {Viktor Bene\v s},
title = {Extremal and optimal solutions in the transshipment problem},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {33},
year = {1992},
pages = {97-112},
zbl = {0754.60008},
mrnumber = {1173751},
language = {en},
url = {http://dml.mathdoc.fr/item/118475}
}
Beneš, Viktor. Extremal and optimal solutions in the transshipment problem. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 97-112. http://gdmltest.u-ga.fr/item/118475/