I have a MIP minimization problem where I have a maximization in the constraints:
$$\max(c_1x_2,\, c_2x_2,\, \ldots,\, c_nx_n) \geq q$$
- $c_n$ constants
- $x_n$ binary variables
- $q$ constant
$x_n$ is not part of the objective function. How can I linearize this?
The first step to solve this would be to create a new variable $z$ representing the the maximum value. Further I think a Big M should be used. But what would become the constraints?
I found an option that almost does this but it is for two variables instead of $n$. For example $\max(x,y)$.
Furthermore, this problem is similar but doesn't cover the problem exactly.