On cycling in the simplex method of the transportation problem

Włodzimierz Szwarc

On cycling in the simplex method of the transportation problem

Włodzimierz Szwarc

Applicationes Mathematicae (2009)

Volume: 36, Issue: 1, page 59-73
ISSN: 1233-7234

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Abstract

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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.

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Włodzimierz Szwarc. "On cycling in the simplex method of the transportation problem." Applicationes Mathematicae 36.1 (2009): 59-73. <http://eudml.org/doc/279951>.

@article{WłodzimierzSzwarc2009,
abstract = {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.},
author = {Włodzimierz Szwarc},
journal = {Applicationes Mathematicae},
keywords = {transportation problem; assignment problem; cycling; basic solution; node; link; directed weighted tree},
language = {eng},
number = {1},
pages = {59-73},
title = {On cycling in the simplex method of the transportation problem},
url = {http://eudml.org/doc/279951},
volume = {36},
year = {2009},
}

TY - JOUR
AU - Włodzimierz Szwarc
TI - On cycling in the simplex method of the transportation problem
JO - Applicationes Mathematicae
PY - 2009
VL - 36
IS - 1
SP - 59
EP - 73
AB - 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.
LA - eng
KW - transportation problem; assignment problem; cycling; basic solution; node; link; directed weighted tree
UR - http://eudml.org/doc/279951
ER -

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