Three-way matching: why it should be a gate, not a report
Order, receipt, invoice. If the three disagree, nothing should be paid. The problem is that in most systems this is a report.
Three-way matching compares a supplier invoice against the purchase order and the goods receipt on price and quantity, so nothing unordered, undelivered or differently priced gets paid. Where incoming inspection applies, matching uses the accepted quantity, making it a four-way match.
Gate versus report
In most systems three-way matching is a report: the invoice is entered, posted, and someone opens a discrepancy report at month end. By then the payment has gone out.
The right design makes matching a gate. An invoice linked to an order cannot be approved until validation has run, and exceeding tolerance requires an explicit written reason.
The fourth way: quality
Suppose a hundred pieces are received and eight are rejected at inspection, while the supplier invoices for a hundred. Three-way matching passes it, because the receipt says a hundred. Four-way matching does not, because only ninety-two were accepted.
Quietly paying for rejected goods is one of the most common invisible losses in manufacturing.