3 way matching is to compare three documents i.e.,
1. Purchase order
2. Receipt of Items/Packing slip
3. Invoice.
For example, if we Order for 50 Items in purchase order and received 40 Items
only instead of 50 items. But we received invoice for 50 items. After comparing
the three documents we pay for only 40 Items..

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Invoice has to be matched with received amount of the PO.
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You have to match the invoice with the purchase order and packing slips.
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3 way Matching is matching with PO, Invoice and GR

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3 Way of matching means we compare the invoice with purchase order and our material receipt note from stores. Similar event is also matched with other two supporting in business.
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Quantity/Price Ordered should match with Quantity/Price Recieved and Billed is known as Three way match. If the Quantity received and billed is lesser than Qty Ordered is fine to proceed for payment, it should not cross Qty Ordered in any circumstance.
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2, 3 & 4 way matching process followed in PeopleSoft.
Two-way matching compares vouchers and purchase orders if the Receiving Required option for the purchase order is Do Not Receive or Optional.
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Three-way matching compares vouchers, purchase orders, and receipts if the Receiving Required option is Required and the Inspection Required option is not selected for the receiver.
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Four-way matching compares vouchers, purchase orders, receivers, and inspections if receiving is required and inspection is required.
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Receipt-only matching compares vouchers to non-purchase order receipts.
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