There are two kinds of supplier invoice from a payables point of view, and the difference between them is a single reference. An invoice quoting a purchase order can be compared against what was agreed and what arrived, and can clear with almost no attention. An invoice quoting nothing is a claim that has to be investigated by a person, and it is many times more expensive.
What the reference unlocks
It connects the invoice to the order and, through it, to the goods receipt. That allows an automatic comparison of supplier, price, quantity and total, and an automatic clear within tolerance. Without the reference none of that can happen, regardless of what software you own, because there is nothing to compare against.
What happens without one
Somebody has to establish what the invoice is for, whether it was authorised, who should approve it and which cost centre it belongs to. That is research, it involves at least one other person, and it is why organisations commonly return unreferenced invoices to suppliers rather than absorbing the work quietly.
Getting suppliers to quote it
Tell them, consistently, and say what will happen if they do not. Most suppliers comply readily because their own collections process benefits from a reference too. The internal half is harder: making sure orders are raised in the first place, which is a purchasing behaviour rather than a supplier one.
Questions people ask about purchase order invoice
Should we reject invoices without a reference?
Many organisations do, returning them for reissue. Decide it as a policy and communicate it in advance, or it just generates angry calls.
What if the supplier quotes a wrong reference?
Treat it as an exception with a reason rather than guessing. Correcting the reference with a note is better than paying against an assumption.
Do all purchases need an order?
Most organisations set a threshold. Below it, invoices are approved on their own merits, and the volume of those is worth watching.