I have a minimization function which is in its simplest form looks like below. I am including the index of the variables.
min cost * Z S.t. Z >= max(a1, a2, a3,....aN)
where Z and a's are variables. Since this is a minimization, I wrote a constraint in AMPL, that goes through the index of these variables and enforces the following.
Z >= a1 Z >= a2 ...... Z >= aN
However, Z is set to a value that is greater than the maximum of a1, a2,....., aN. Please let me know how can I optimize this formulation so that Z is set to exactly the value of the max (a1, a2,....,aN). Do I need to use big-M formulation to do that? If yes, how do I do that?