I was told this is how it works, not too sure how accurate it is. The driver will come in, get a list of pick ups they have to do and the pick up deadline. Then the list of packages they gotta deliver during the day, as well as deadline for them. So everything they deliver is usually check out already in the morning, ignoring special circumstances like rush packages.
Now I know for a fact that post office work very similarly, the carrier comes in during the morning, grab the letters, sort to ensure it's their route and in the order they like it to be, then haul ass to deliver them before their shift end.