I use the standard AMPL IDE for solving LP and IP problems. Using the AMPL IDE, is there a way to implement the cutting plane approach to solve IP problems i.e., separate (using a suitable separation algorithm) violated constraints (which are in exponential numbers and are not part of the original model to start with) and add them on the fly as required?
You could check out our Benders decomposition examples, which successively add cuts and re-solve; they are at Additional Scripts: Looping and Testing – 2 on our website. The implementations use AMPL scripts, which can be run from the IDE.