Is there a method for the simplex algorithm that avoids cycling?

[wanderlust.xx]

Homework Statement

"There exists an implementation of the simplex algorithm that avoids cycling. (If your
answer is `yes', describe the strategy; if your answer is `no' give an example and explain
briefly why every strategy must fail.)"

The Attempt at a Solution

We normally do the simplex algorithm using the largest coefficient rule for the entering variable.

I would assume that to avoid cycling, we simply change this to another procedure, although I have tried to research this in both a book I have here and on the internet to no avail... I'm not sure how to go about doing this question! :(

 

[Ray Vickson]

Look up "lexicographic ordering" and "Bland's Rule".

RGV