The following will guide when to mark an Inventory Record as Incomplete vs Complete when you've Received a lesser quantity than was Ordered. 

This will ONLY apply when the lesser quantity is either sufficient for what is needed OR the remaining (backordered) quantity will be moved to a new Purchase Order and, therefore a new Inventory Record.

As a general rule of thumb, the rule is as follows:

Stock PO:  COMPLETE (then update the PO Quantity)

Special Order PO:  INCOMPLETE (then clear the backorder)

Stock POs should be Received as Complete when the lesser quantity Received is sufficient. Since a Stock PO is not generated directly from a Job/Project, it has no pre-existing quantity commitments, so marking it as Complete will communicate to the Inventory Module that the quantity Received is all you are anticipating.  In most circumstances, once you've clicked "Complete" you'll be prompted to select whether you want to update the PO Quantity as well. Select "Yes" so that the Purchase Order quantity will match what was Received, otherwise the Purchase Order will remain in the "Partially Arrived" status. 

Special Order POs should be Received as Incomplete when the lesser quantity Received is sufficient, even though the remaining quantity will not be Received against this record. Since the PO is generated directly from a Job/Project, there is a pre-existing quantity commitment, and marking it as Complete will have no effect. For this reason, you'll mark it as Incomplete, then proceed to Clear Backorder on the record. Clearing the Backorder is the step that communicates to the Job/Project from which it originates that the quantity Received is sufficient and will update the Working Quantity to what was Received. 

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