fixing sagging insulation
You have several issues: 1) hold the insulation in place, 2) vapor barrier, 3) vent space above the insulation 

1) I’ve seen string installed across the joists to keep the insulation from falling down. They usually install it about 6” apart at the ends of the batts and about 12” - 16” apart elsewhere. You can staple the string to the bottom of the joists. 

2) Using string will not provide a vapor barrier. If you use poly sheeting stapled on the bottom of the joists, it will provide a vapor barrier. Depending on where you live, you may not want a vapor barrier. 

3) The Code requires a 1” air space above the insulation. That is to say, you must maintain a 1” air space between the bottom of the roof sheathing and the top of the insulation so air can circulate. (You’ll need to verify that attic vents are installed so you don’t get condensation in the attic.)