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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August 20, 2009 at 8:44 am
Anshu
The number taking approach reminds me of your typical government service office (where you’re holding number 238 and the sign says “Now serving number 56”).
I also do prefer to watch as my groceries get scanned as errors in pricing (the item scanning for more than the posted price) is still too common for my liking.
August 20, 2009 at 11:18 am
Mario
I like the idea, but I think stores would be too afraid to lose impulse sales to try it out. Customers may not like it, but stores often benefit from (slightly) longer lines.
August 25, 2009 at 11:36 pm
Diego Navarro
I didn’t read TFA, but have argued forever that supermarkets should have “discount lines” – specific cashiers with 5% and 10% discounts on the total amount of the purchase. The prevailing level of prices can be raised to compensate, and people less willing to wait may as well be willing to shell out a few extra bucks to get to work in time.