perhaps this would be better suited for the cardiology or internal medicine board, but i think the most straight forward answer is that a CABG (coronary artery bypass graft) is in order when there's a substantial blockage of the artery.
Oftentimes, patients may receive a angioplasty (ballooning of the vessels) or a stent (spring-loaded meshwork that pushes built up plaque against the walls of the vessel) before having a CABG. An initial step in this entire process is often an angiogram, where the cardiologist will shoot dye through the blood stream and observe if blockages do occur, and if they do, to what extent.
I'm pretty sure there's some specific criteria for stress tests and ejection fractions, but I dont know them off the top of my head.
One criteria is blockage in multiple vessels. (I think the specific number is 3 vessels). In that case CABG is preferred over angioplasty. Also, if the patient has very poor L. ventricular function because of the MI.
The American Heart Association publishes guidelines on this topic. They change from time to time (and I believe a new revision is coming out soon given the data on late thrombosis with drug eluting stents). But, look up those guidelines. They are quite specific.