Suppose I have the following set of binary variables:
$X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$
$Y_j$: $J$ ranges from {1,..,3}
$Z_k$: $K$ ranges from {1,2} lowest priority among the three variables $X$ , $Y$ and $Z$
How can I formulate the following :
(1) If any variable $Z_k = 1$ for each $k\in K$, Then each and every $Y_j$ variables $y_1$, $y_2$, $y_3$ must first $=1$
i.e. $y_1 = 1$, $y_2 = 1$, $y_3 = 1$
In other words, before any $Z_k$ for each $k\in K$ $=$ 1, all $Y_j$ variables must FIRST = 1
(2) SAME APPLIES FOR THE RELATIONSHIP BETWEEN $X$ AND $Y$ variables
If any variable $Yj = 1$ for each $j\in J$ Then each and every Xi variable $X1$, $X2$, $X3$, $X4$ must first $=1$
$x1 = 1$, $x2 = 1$, $x3 = 1$ , $x4 = 1$
In other words, before any $Y_j$ for each $j\in J$ variables = 1, all $Yj$ variables must first be = 1
I'll write an example just to make sure I was clear:
Before $y_2$ is picked and is = 1, All $x_i$ for each $i\in I$ must equal to 1. Meaning that X variables are at a higher priority than y variables and should be picked first.