I studied that to choose the leaving variable in simplex method , we need to find the pivot row . To find the pivot row , we need to use Minimum Ratio Test . And according to this test , the pivot row would be the row with the smallest positive number . Let's say I had 0 , 50 and 200 . So the pivot row is the row with " 0 "? I tried to do the gauss jordon method with "0" , but it keep cycling and make me confuse .
2026-02-22 22:48:10.1771800490
Does zero considered as a leaving variable in simplex method?
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Yes, a row with ratio 0 would be the pivot row. A zero ratio signals a condition called degeneracy. Google "degenerate solution linear programming" to find out more. In geometric terms, there are more constraints binding at the current vertex of the feasible region than the number needed to define a point. (You need one binding constraint for each decision variable, excluding slack and surplus variables.)
When the simplex method arrives at a degenerate corner, cycling can occur. There are a variety of adjustments you can make to the basic simplex algorithm to avoid being stuck in a cycle. See the relevant Wikipedia page for a brief discussion.