I run my minors differently. A ham sammich can make AAA on my teams. I always try to promote from within and rarely if release a player.
Day 1 after the budget are set, I go to the GM office to my AAA team and double check all batter's positions. (click on position, click show recs (proj.) and ok). Then I promote from AA the guys I need to fill (after checking their positions). Wash, rinse, repeat all the way to Low A. I only promote pitchers at this time that are prospects, make sure that there is 5 starters, and to bring my pitching staff to 11 players.
I keep 14 batters and 11 pitchers as active players. If there are any holes at that point, I go find my 6 year minors FAs and resign them before the open FA signing.
Once the season starts and the relievers get tired, I go down a level and start bringing up the "better stat" pitchers from the previous season and inactivate the tired pitchers. Then there is a pool of pitchers that can get swapped in and out.
In general I find 5 inactive pitchers to be enough, but if I end up having a lot of high durability guys, then it can be as little as 2 inactive pitchers. But right now in Ryan my AA has 10 inactive pitchers due to low durability and it is an extreme hitters park.
Oh, if a batter gets hurt, I will go 13 batters and 12 pitchers. If there are multiple batters hurt, then I promote or sign someone from the junk pile.