Hmmm ... several issues. First, let's make a distinction here between two different situations.
Case #1 is customer comes in with two or more complaints and we can fix some but not the others. For instance, line one glove box is loose; line two door molding is loose. We adjust the glove box in line one and order a molding for line two. In this case, I don't know of any reason under the sun why you wouldn't close the ticket. Get paid for glove box today and for the molding when the part comes in on another R.O.
Case #2 is when we are continuing a repair/ diagnosis. Customers complains of window in op - we diag a switch and relay - we have the switch but not the relay. In this case, I might, *might*, see a reason to keep the RO open. But I'd rather, set the switch aside in SO parts until the relay comes in, close it N/C and make a copy to remind us to flag for any previous diag when the job is complete.
The only way either option would impact your numbers is if you submit for the diag twice when you separate the repairs.
If Honda tells you to leave ROs open I would like that clearly spelled out in writing to show to my manager. We have a former big-wig Honda auditor on staff I can ask his opinion as well. Generally leaving an RO open demostrates a vehicle out of service and opens up a potential lemon law more than a N/C ticket. Again, the only thing I can think of is that they would not want you to submit for diag today and the repair tomorrow. A claim generally should never be submitted until the repair is complete.
A N/C ticket shouldn't generate a CSI or follow-up phone call. And dollars per RO would actually go down if you're opening more than one ticket. It depends on Honda's evaluation criteria to know how it would imapct you.
With a few exceptions, my thoughts are if I can't walk out an physically put my thumb on the car on our lot, then a ticket shouldn't be open. Open ROs are primarily for vehicles at the store waiting to be fixed.
But hey, that's just one person's opinion. I could be wrong

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** Rob, Editor WD&S **Help is only a message post away!
robc@dealersedge.com