Question

Where to use simplex and where should i use two lhase simplex?

Answer 1

The big-M method is not an algorithm but a formulation trick to model discrete decisions in the context of a mixed integer program (MIP). As such, it is impossible to say how fast it is relative to an actual algorithm such as the simplex algorithm. However, MIP formulations with big-M's usually do not solve quickly and problems that are purely linear (no integer variables) will solve quickly.

As a side note, whenever you make a big-M formulation for a problem, M should be large enough, but no larger than that, as very big M's lead to very loose linear programming relaxations.

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