This piece from the manual is very informative:
Each turn, supply points (both General Supply and Ammunition) are produced and stored in friendly-controlled
cities, ports, fortifications, and depots. Supplies are produced and distributed on the first day of each game turn
and generated solely in basic or full SC increments The number of full or basic SCs produced by a structure depends
primarily on the level of the structure, but other factors modify that number..
The countryside of a region generates 0-4 basic SC to
unbesieged units (depending on civilization level, weather
and looted status). When enemy armies co-exist in the same
region, the region’s supply is distributed in proportion to the
percentage of military control. For the moment there is no
cavalry, light troop or irregular advantages to foraging.
Level 1 cities and Raider villages generate 1 basic SC.
Unbesieged level 2 (or +) cities, all fortifications, depots and
unblockaded harbors generate full SCs as follows
1 / city level
1 / port level
5/ fort level if there is a fort in the region
10/ depot level if there is a depot in the region
SCs do not accumulate from one turn to another: they only serve to replenish units and Impedimenta in the same
turn. Any surplus is lost.
You might say, supply never replenishes, it is just there each new turn. Note that forts, not castrums, add to the calculus. But you never 'build' supply beyond the numbers above.
Unlike most other AGEOD games, supply is not forwarded from depot to depot. Supply is made and consumed in the same region.
I try to match armies to the current supply of the region the army is inhabiting. The one way you can extend supply is to run wagons back and forth between the army and another supply source.
From your post I am uncertain of the scope of your question. Are you wondering about supplying troops, rebuilding troops or some other issue.