I have seen some papers claiming that their proposed model is integer-friendly. I would like to get more information about what type of constraints we can call integer-friendly.
Probably, it can be better understood if I have some examples. Here is part of a model in the context of location covering:
\begin{align}&z= \max\sum_i v_i \\\text{s.t}\quad&v_i \geq c_{ij}x_{ij},\quad \forall i \in N, j \in M\tag1\\\quad&v_i \geq 0\\\quad&x_{ij} \in \{0,1\}.\end{align}
where $c_{ij}$ are some positive non-integer constants. My question is:
Why constraint set (1) is NOT integer-friendly, and how can I improve this constraint?
If I define the $x_{ij}$ variables to be continuous in $[0, 1]$, they will be always 0 or 1. Does it help to some extent?