I have a silly confusion.
For this constraint here, $a_{i1,j1} + a_{i2,j2} ≤ 1$ if $0 < |i1−i2|+|j1−j2| < d$.
I understand this constraint but I want to ensure that this encompasses all $i$ and $j$, not just $i1,i2$, and $j1,j2$. I am told that this constraint in fact, encompasses ALL $i$ and $j$, but I am NOT getting it.
Also, can we have 'if' in a programming constraint equation like this? I am trying to find an example but failing at that.
Please help.
This is actually not one constraint, but rather a set of constraints, one for each $(i_1, i_2, j_1, j_2)$ satisfying the condition $0 < |i_1 - i_2| + |j_1 - j_2| < d$. The "if" clause is not part of the linear programming problem itself, it just determines what constraints that problem has.