Does anyone has any invoice checking process for warehouse/3PL invoices? Checking invioce vs contract?

Yes, per cost category defined.
Are you looking for automated solutions or simply if someone has this process in place?
As we could not fully automate this, we semi-automated it in Excel as the data load for us is not huge behind.
We have a matching contract with the 3PL of course that they itemize the costs per activity (activity based costing) and it goes behind every invoice we need to pay.

This is not a perfectly matched response as we do not utilize 3PL services. However, posting this for possible overlap or interest. Our hybrid vendor management office and financial accounting teams issue Purchase Orders upon the execution of any contract. When an invoice comes in, it is tied to the Purchase Order to confirm the amounts are within contract. Further, non-fixed fee strategic vendors (e.g., data providers that bill at the transaction level) are reviewed by a role that compares directly the contract and invoice, and internal data on usage, to confirm invoice validity.