Some of the trade-offs, both mathematical and psychological are discussed in this article from The Numbers Guy.  My favorite idea:

Dilip Soman: “I have a radical solution. Once a shopper is ready to check out, she wheels her cart into an area where she gets a number, and is directed to a lounge. Staff members scan and generate ‘invoices’ and once ready, the numbers are called out into the lounge area so that the customer can pay. The one thing that I don’t know is whether customers will feel some anxiety about not being in front of their groceries when they are being scanned, but if they don’t, I think this will be the most efficient solution!”

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