I have a problem which is mainly linear but it has a non-linear component. The objective function is
obj = Linear_term + $c*f(x,y)$ where,
$f(x,y) = (G_1 x_1 + G_2 x_2)/(x_1 + x_2)$.
The decision variables and parameters are as follows.
$0 < b_1 <1$ :: decision variable
$0 <b_2 <1$ :: decision variable
$c>1$ :: integer decision variable
$Q_1$ :: constant
$Q_2$ :: constant
$G_1$ :: constant
$G_2$ :: constant
$x_1 = Q_1 * b_1$
$x_2 = Q_2 * b_2$
My questions are:
How I can model $cf(x,y)$ in MIP? Please note it is also probable that more than two decision variables of $b$ appear in the last equation.
How do I break this fraction and model it in linear form?