I am still unclear about when the inventory is updated and how we ensure that inventory corrections are made.

I understand that process as follows - please correct anything I have got wrong:

1. We raise a PO in QBO and send to vendor.
2. We raise a Bill to match one or more POs.
3. Vendor makes full or partial shipments against each PO.
4. We check packing slip against PO. Vendor may also notify on packing slip items unable to be fulfilled. Vendor may have issued some items short of or over the number we ordered. What action should we take in QBO at this stage for each of these variations?
5. Vendor sends an invoice which may be for an entire PO or for one or more partial shipments. This includes shipping cost for items covered by that invoice.
6. We add the shipping cost to the related Bill in QBO. Each Bill may end up with several lines for shipping cost.
7. We pay the invoice and apply it to the Bill. Even when that vendor has completed all shipments for a PO, the Bill total may not match the total of all invoices (usually the total of all invoices will be less than the Bill total.

(Note that I have not included a reference to the situation where a packing slip is incorrect as obviously we talk to the vendor and sort out how to resolve it.)

Once we know that the vendor has finished issuing invoices against a PO and all invoices are paid, QBO still shows an outstanding amount due on each Bill. Presumably there is also a discrepancy between the inventory added in accordance with the Bill and the actual shipments received (on packing slips). How do we ensure in QBO that the inventory adjustment, the PO, the Bill and the goods received all match at the end?

Thanks in advance for any explanation and advice. This is causing a lot of stress because it is over 6 months since taking over the accounting for this and Bills are not being cleared and Inventory is going out of whack!