We do exactly what you would do if you're being completely proactive...just behind the scenes so you don't have to worry about it. We call the pizza place, call the driver, deal with the annoyance. You just relax and wait for your pizza.
The customer knows if it arrived - do they need to notify you when it does? Or do all the services notify you? Otherwise, I don't see how you can tell if it's late and likely got misordered, and you need to contact the pizza place again.