I was wondering if the type of variables, whether binary or non-negative can affect the linearization?
For example assuming that $x_{i,j,t}$ and $y_{i,t,s}$ are two binary variables, then when we want to linearize $ \sum_{i,j} x_{i,j,t} \ge 1 \implies \sum_{i} y_{i,t,s} \ge 1 \quad \forall t,s$ then could we say? because they are both binary: this is equivalent to $\sum_{i,j} x_{i,j,t} \le \sum_{i} y_{i,t,s} \quad \forall t,s$?
(note that the $i$ in the left and right should not necessary be the same, I just want having for one $i$ , $y_{i,s,t}=1$)
Or we have to use indicators like $\delta =1 \implies \sum_{i,j} x_{i,j,t} \ge 1 $ and then $ \delta=1 \implies \sum_{i} y_{i,t,s} \ge 1$
I knew that if $x,y$ were not binary, we should use indicator trick, but it is necessary here??