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# Wydawnictwa / Czasopisma IMPAN / Applicationes Mathematicae / Wszystkie zeszyty

## On cycling in the simplex method of the transportation problem

### Tom 36 / 2009

Applicationes Mathematicae 36 (2009), 59-73 MSC: 90C05, 90C08, 90C27. DOI: 10.4064/am36-1-5

#### Streszczenie

This paper shows that cycling of the simplex method for the $m\times n$ transportation problem where $k-1$ zero basic variables are leaving and reentering the basis does not occur once it does not occur in the $k\times k$ assignment problem. A method to disprove cycling for a particular $k$ is applied for $k=2,3,4,5$ and $6$.