# What is the "big-M" method? And are there two of them?

I’ve seen the "big-$$M$$ method" referred to in different ways. What is the "big-$$M$$ method" and why does it seem to mean two different things?

• just a suggestion to improve the post, perhaps it would be better to include examples where they seems to mean different things? Jun 2, 2019 at 5:18

People do use the term "big-$$M$$ method" to mean two different things. In both cases, the name refers to the use of a large constant, often denoted $$M$$.
Sometimes people also use the term "big-$$M$$ method" to refer to the use of big-$$M$$ parameters in logical constraints in (mixed-)integer programming problems. For example: if $$x$$ is a continuous variable and $$y$$ is a binary variable, then the constraint $$x \le My$$ says that if $$y=0$$, then $$x$$ must equal 0, and if $$y=1$$, then the constraint places no restrictions on $$x$$. Note that in this case, it’s important not to choose a value of $$M$$ that is too large.
Aside: I highly recommend @prubin's excellent blog post on big-$$M$$ in all its forms.