All in southern Chicago? How far apart? How long does it take for them to pop out of the machine, from completing the spec? It sounds to me as if they are assembled at the mentioned central location and sent to the vending machine via a pneumatic tube. The only unlikely part is that this wouldn't require anything like the bulk of three coke vending machines for the end user terminal.
Afetr all, with RFID tags pneumatic tubes get routing capability, as the destination of a shuttle can be read as the shuttle whizzes by. So it's perfectly easy to have a city wide pneumatic tube infrastructure. But it would have to be fast to be viable.
All's technically feasible. It's the humans that are the problem. Time to exterminate them.