I have a constraint like this:
$$\sum_{i \in I} \; d_{i} a_{ij} \leq c_j x_j \; \; \; \forall j \in J$$
with $d_i$ and $c_j$ as a constants and $a_{ij}$ and $x_j$ as decision variables that are binary. So the question is how could I represent this in a CPLEX linear program?
If we take $J = \{1\}$ and $I = \{1,2,3\}$ with $d = \{10,15,16\}$ and $c = \{20\}$, for the moment I am writing something like this as my CPLEX constraint:
10 a_1_1 + 15 a_2_1 + 16 a_3_1 <= 20 x_1
But with this I get an error like this:
invalid symbol(s) beyond right-hand side
As I know, we can't do division in CPLEX (if I am not wrong), so is there a way to fix this?
Best Answer
You can move all the variables to the LHS: $$\sum_{i \in I} \; d_{i} a_{ij} - c_j x_j \le 0$$
But I don't think that is required. Maybe you just forgot a semicolon.