On cycling in the simplex method of the Transportation Problem

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=2,3,34,5 and 6.Transportation Problem, Assignment Problem, cycling, basic solution, node, link, directed weighted tree.