Cost index has nothing to do with being on time. It is about fuel burn. Strong headwind high cost index. Tailwind low cost index. Plane does not know on time. Plane knows efficiency. Example. If you are late and have a tailwind you will still see a low cost index. It is up to pilots/dispatchers to increase this to get back on time. Increased fuel burn. Manual says stick to the planned as much as practical. If I am early I play with the number/altitude to see if fuel burn goes down. If I am trying to make a commute it goes 99. Just kidding of course. Some pilots insist company monitors what you put in and will get in trouble.

I always try to save fuel. Not so much for company but for my own personal fun. Same as when I drive my cars. I kick my wife’s ass in efficient driving. She is a much better driver than I am but less efficient. I have been a hyper-miler since I started driving.