At AA, we have trip ownership and are assigned trips based on buckets of days available. If you have 3 days of availability, you're in the 3 day bucket and will get a 3 day trip if your number gets called. They can assign outside of the bucket, but that's only if everyone in that bucket was already cleared out. Once you get the trip, it's yours. If you get re-assigned for any portion of that trip that you are qualified, legal, and available for, you get paid premium for that portion.
They can breakup a trip that hits open time however they want and turn a 4 day into whatever they want, but this isn't that efficient.