Optimising Routes

I have an interesting query involving moving vehicles around and optimising the drivers over those routes.
I'm not sure this is even a sensible process to try and manipulate in Access but I thought I would ask as there are some very clever people in here

Given the following data what would be the most efficient way to carry out the trips - ultimately there aren't enough movements between the various sites for a perfect solution, but what would minimise the amount of "dead end" trips...

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