Green's official ailment is a "left hip labral injury," which has held him out of action since it happened in batting practice last week. Because he hasn't appeared in a major league spring training game recently, the Brewers can put him on the DL retroactive to March 22 and he'll be eligible to return as soon as April 6 if he's healthy and the team has a spot for him.
Rogers' velocity loss, meanwhile, has led to him going on the DL with "right shoulder instability." He last pitched in a major league game on March 24, so he'll open the season on the DL retroactive to the 25th. If his velocity returns and the team needs him he'll be eligible to pitch as soon as the April 8-10 Cubs series.
If Rogers had options remaining the team would probably consider sending him to the minors to work on these problems, but because he doesn't the team had to either put him on the DL, keep him on the roster or put him on waivers.
The beneficiaries of these moves are probably Donnie Murphy, who now appears poised to make the team as a backup infielder, and the pitchers vying for the final bullpen spot.