TITLE: Simplex algorithm — primal or dual?
QUESTION [9 upvotes]: As far as I know there are two simplex algorithms – primal and dual. They have different halting criteria etc. Before using simplex I have to make a standardization of the LP. So, when do I use primal, and when dual simplex?

REPLY [2 votes]: Adding to what was said above, the dual simplex algorithm is also very useful in cases where you might need to $\textbf{insert new constraints}$ as you go.
Using the "regular" simplex method, you would have to solve the problem from the beginning every time you introduce a new constraint, and using the dual you will only have to make some (relatively) minor modifications.
See example here.
BTW, using the dual simplex method is equivalent to taking the dual and then using the simplex method on the dual. See example here.