how to apply Big M to model the logic constraint （if-then-else）

Question

I was hoping to get some help in modelling the following logic as an MIP Constraint

c_{m,l}^{RC} is binary decision variable. Simplify it：

Answer 1

You want to model $y=1 \iff x > 0$. The following big-M constraints enforce that relationship, where $\epsilon>0$ is a small tolerance: $$\epsilon y \le x \le M y$$

Because your $x$ is integer, you can take $\epsilon = 1$.