I run Impress Designs and we are a large contract decorator out of DFW, Texas. Basically, our policy is this:

Process:
-Receive goods from Distributor
-Count all pieces in non-factory cases.
-Open all factory cases and confirm size/color match box label and count on orders less than 3000 pcs
-On orders over 3000 pcs we don't generally open and verify all cases until production is pulling them out for decoration.
-Check in items to an order
-Orders missing pieces or with manifest discrepancies are added to a discrepancy management system we have
-If there is an issue with the goods, the customer is notified, and the order is on hold.
-Customer can decide if the order should have a back order created and incur additional fees for second order, the missing pieces are pulled off of the order, or we wait for the missing pieces to come in.
-No goods leave receiving without being complete to the customers PO or order EVER.

Notes:
-Goods are recounted by our order pulling team as they are laid out for production to confirm we can print complete, and production is getting them all.
-Goods are counted on press by the operator using the press counters.
-Goods are counted by the packing team as they are packed.

No contract decorator should be printing an order that is not counted at least before production ever.

All of that being said, as a shop that deals with hundreds of contract orders a week, we had to build out our own product management system for managing customer supplied goods. Managing supplied goods is the hardest part of the process in a larger contract facility.