Re: Linearize the "if" in AMPL

[Paul]

This depends on whether N1 and K are variables or parameters and, if variables, whether they are integer or continuous. You might find some clues in this blog post.

Paul

[Paul]

I'm going to omit indices just to reduce typing. Let M be a parameter giving a valid upper bound for N1 and let z be a new binary variable. Add constraints
NB <= K, NB <= N1, NB >= N1 - M*z and NB >= K*z. (I'm assuming K, N1 and NB are all nonnegative.)

If the rest of the model pushes NB to be as large as possible, you only need the first two constraints (no M, no z).

Paul