This paper shows that cycling of the simplex method for the m × n transportation problem where k-1 zero basic variables are leaving and reentering the basis does not occur once it does not occur in the k × k assignment problem. A method to disprove cycling for a particular k is applied for k=2,3,4,5 and 6.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-5,
author = {W\l odzimierz Szwarc},
title = {On cycling in the simplex method of the transportation problem},
journal = {Applicationes Mathematicae},
volume = {36},
year = {2009},
pages = {59-73},
zbl = {1156.90415},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-5}
}
Włodzimierz Szwarc. On cycling in the simplex method of the transportation problem. Applicationes Mathematicae, Tome 36 (2009) pp. 59-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am36-1-5/