If I am in your position (which is rarely impossible), I'll not instruct to every staffs that the limited time to put every concerned documents which we need GM's signature must be within 3:00pm otherwise, you won't accept to put on your desk and also our staffs can't stand at your desk to rush you to sign (you usually say: don't pressure). And before you go home, you usually keep the document tray in your personal cabinet and don't allow staffs to put any document on your desk, why? What do you want management to know? (no pending issue?) Is this the management's thinking?
How can our staff do? with the limited time of cut-off billing with customer? If you are in our position (which you used to be), what will you do?
If my solving the solution like this is mistake, I'm willing to accept your and management punishment, because if we fail of billing cut off date, I also must get the complain from management as well.
Sorry to say and reply in the impolite manner, but this is the truth from our staffs's mind.