The ID cards idea is very old and has been contemplated by the govt. many times, but they havent implemented it, because there are so many people in Mumbai who even dont have ration cards, consider the thousands of homeless poeple in Mumbai.
I like the second idea, the entry/exit doors thing, but even if you do that, it wont be possible for the police to catch the culprit in a city of millions. Well, its not impossible but surely challenging.