It is really very simple to adjust actual supply to actual demand. You follow the amount of goods and services utilised and compare it the amount of goods and services produced.

If there isn't enough of a product you find a way to deal with the shortage and communicate back to the producers to up production if at all possible.

There will be no room for corruption because it will be organized democratically, i.e. open and accountable, everyone with equal say. In society without private property there will no advantage in accumulating goods, because they are available free to everyone.

There will be no need for cops because most crime is private property related, the rest we could deal with ourselves.