sci.op-research

sam.b wrote:
> How to explain that a new entering variable with negative reduced cost
> has still a negative reduced cost once it's in the basis ? Is it a
> kind of degeneracy ? Because in this case the same column will be
> selected in the next iteration. Simplex problem ?
> Thank you.

Not possible (other than perhaps rounding error, i.e. reduced cost =
-0). The reduced cost of all basis variables is zero.

If the new variable has a (nonzero) lower bound, imposed as a bound
rather than as a constraint, it can hit the lower bound and still have a
negative reduced cost; but it won't be basic in that case.

/Paul