I have never seen a formula for determining this, but have heard of companies that specialize in analyzing this. It is a difficult question, as each branch has different needs. While the cash balance at the branch may seem adequate, it may not be in the needed denominations. Many branches take in, for example, mostly large bills, but their customers want small bills back. They end up selling to the main bank and buying other denominations that they need. The best way to determine this is to look at historical records. Make the operations manager at the branch responsible for keeping vault cash as low as possible. When you end up making extra cash runs frequently, they do not have enough cash (or correct denominations) on hand. Seasonal issues also affect this, such as tax time, Christmas, etc. While I wouldn't say to wing it, I would suggest an "educated guess". Hope this helps some.
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Newbie Mgr