I would like to seek some advice on modeling the following:
I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is to be equated to a third integer decision variable, $z$, which is also equal or greater than zero in accordance to the value of a binary indicator variable, $\beta$.
$\beta=1$ $\implies$ $x=z$
$\beta=0$ $\implies$ $x'=z$
Appreciate your kind guidance.