Suppose we have two continuous nonnegative variables $X_{1}$ and $X_{2}$ both bounded by the number $M$ from above.
I would like to model the following:
If $X_{1} > 0$ then $X_{2} = 0$
If $X_{2} > 0$ then $X_{1} = 0$
I can do this by imposing $X_{1} X_{2} = 0$ but this is a nonconvex nonlinear term.
I can instead model as follows:
$X_{1} \le M \\ X_{2} \le M \\ X_{1} \le B_{1} M \\ X_{2} \le B_{2} M \\ B_{1} + B_{2} \le 1 $
where $B_{1}$ and $B_{2}$ are binary variables. The result is a MILP.
Can you see an alternative way for modeling this relation?