I don't quite follow.  Your currently part-paying invoices based on what was actually shipped to you, correct?  So can you explain the Vendor's problem in more practical terms i.e. is it that the Vendor has to re-issue a new invoice reflecting the short shipment but instead they just want you to pay what was received and handle the accounting by adjusting the original PO or something then have you issue a RCTI, or does the Vendor want you to pay the full amount up front and handle the short shipments via credits or something?

I could be very wrong but it sounds like the Vendor is being lazy to me, its their problem they keep short shipping you, and they should make things easy for you as you're the customer and surely don't want you changing suppliers?  I think what you're already doing is correct and you shouldn't have to change your processes just to fit in with them - what do yo think?

You are so correct! They are being lazy (as my colleagues and I have thought from the beginning!) I believe the biggest problem is that their accounting is outsourced overseas. They want us to pay the invoice as they have it but add a line item deducting the amount that we won't be paying. It is more work for us, and they've "claimed" they will be removing that practice in the new year, but they are a necessary vendor so we are trying to make it work. Since we use our purchase order and receiving to match what we received to pay the invoice, there is no place to add a line item, that I can see.