Remember, there are probably three or four people involved in that process (the person who receives the order, who then tells somebody to go find the part, who then gives that part to somebody in shipping to box it up and mail it out, and then somebody has to do the bookwork -- taking the part off the inventory list, preparing the billing, entering the data in the computer, etc.
They need to update their technology then. Only person that should see that order is the picker (the guy that gets the item from inventory and puts it in the box). Everything else should be automated. It should cost them a matter of cents to get that order out the door.
And yes, I've seen systems like that in action. The pickers hold handheld computers that are on a wireless network. The computer not only tells them the next order items, but also what size box to use and which items to put in each box. When they pick the items from inventory, they use a barcode scanner on the handheld to verify that it is the correct item. The computer automatically does the inventory management. Once the items are in the box (also verified by barcode), they just set it on the conveyor belt where the box is automatically filled with filler, sealed, stamped with shipping information and rolled onto the truck. It's quite cool to behold if you ever get a chance.