so... logistics player would control supply trucks, some light armour + infantry?
I would put forth that the easier although maybe not realistic method we should try for the first PMB would be to assign LOG trucks at the company level. This will allow for each player to directly control a supplies for his units as opposed to one person controlling all LOG trucks. How the trucks are distributed (regardless of method used) will also have to be decided.
For example and looking at NATO, they have only 8 trucks. Off the top of my head I might think that you would want to split them like this:
INF Company gets 1
TNK Company gets 2
ART Company gets 2
AA Company gets 1
HELO Company gets 1
AT Company gets 1
BTW, each side gets access to a maximum of 22000 supply points (FOB + 12000 in trucks) and they go fast. Managing supplies by being careful of which units you rearm or repair is very important. Artillery can drain a side's supplies very quickly!