When to use Logistical command stations?

[Radiant Phoenix]

from a 40k-or-so threatball.

How many homeworlds do you have and which fleet size setting or whatever are you using?

Normal fleet size, one homeworld, diff 8, FS 4/10, AIP ~500, it was released in a CPA.

EDIT: Oh wait, I suppose it wasn't clear: I was measuring using strength, not ship count, because that's the setting I'm using in-game.