I heard that Zynga copied this game. The original is called Tiny Towers. It is exactly the same but with cheaper graphics. It is no surprise then, that they frustrate the players with empty promises about instant re stocking.
I have noticed that when you fire the special worker and then re hire them, more often they do instant re stock.
If the item they re stock requires only one worker, then fire the co workers.
If the item requires 2 or 3 workers, the app will usually assign the wrong one to re stock, and the special one as a helper. This encourages gamers to buy tower money to speed things up.