When I have to write the formulation of an IP, I usually have the choice between writing $i\times j$ binary variables with two indices such as $ x_{i,j} $ or, writing $j$ integer variables $x_i$.
Is it better to use only binary variables but with a higher number of variables or to use fewer integer variables? Does a solver work better with binary variables?
I personally think that the stronger limitation of a variable is the number of variables so I would choose the solution with fewer integer variables. However, I would like to confirm that.
Thank you in advance for your advice! (PS: Tell me if my question is not clear)