Purchase order matching is usually described as a comparison and usually fails as an absence. When teams examine why invoices did not match, the largest categories are rarely price and quantity disputes: they are no purchase order at all, and no goods receipt recorded. Those are upstream problems that look like payables problems, and they are fixed in a different department.
What the comparison does
Supplier, unit price, quantity and total, compared across the invoice, the order and the goods receipt, ideally at line level. Within tolerance, the invoice clears without a person. Outside it, an exception is raised with the reason and the two numbers that disagree, which is what lets it be routed to whoever can resolve it rather than to a general queue.
Why absence dominates the failures
An invoice with no purchase order has nothing to compare against, so it cannot match by definition. An order with no recorded receipt cannot complete a three-way match. Both categories are generated outside payables, by buying without an order and by deliveries nobody records. Counting your exceptions by reason will usually show these two at the top.
Fixing the absences
A purchase order threshold that people know, a policy for invoices arriving without a reference, and making the goods receipt somebody's explicit job at the point of delivery. None of these cost anything and all of them raise the ceiling on what matching can ever achieve. Software applied before them automates a process with missing inputs.
Questions people ask about purchase order matching
Is two-way matching acceptable?
For services and anything without a physical delivery, yes, and it is the correct choice there. Using it for goods removes the check that you received what you are paying for.
What tolerance should we set?
A percentage with an absolute cap is the usual shape. Set it, then review a month of exceptions and adjust from evidence rather than theory.
Can matching happen automatically?
Yes, where all three documents exist and agree within tolerance. That share is capped by your purchase-order and receipt coverage, which is a number worth measuring.