I would like to seek some advice on modeling the following logical condition:
Given two groups of binary decision variables $A_{i}, i=1...n,$ and $B_{j}, j=1...m$.
$A_{i}=1- B_{j}, \forall i, \forall j$
i.e., if one of $A_{i}=1$, all $B_{j}$ must be zero, and vice-versa.
Besides, the above equality constraint, I would like to include tighter cuts, but have only managed to come up with the following:
$\left\lvert B\right\rvert *A_{i}\le \left\lvert B\right\rvert-\sum_{j=1}^{j=m}B_{j}, \forall i$
$A_{i}\ge 1-\sum_{j=1}^{j=m}B_{j}, \forall i$
Thank you!