They're already on it [0]

[0]: http://techcrunch.com/2014/01/18/amazon-pre-ships/

They actually do something like this: Amazon ships stuff to a logistic center close to you when their machine learning algorithms decide you're likely to buy a specific item shortly.

T "We thought you may be running low on toilet paper, so we sent some for free. If you're not, then just tick no and we'll take it back, or [from a comment that was deleted shortly after it was posted] pass it to an Amazon neighbor for a $2 credit."

T+1 "We've noticed you appreciate our pre-emptive notifications, and hope we've been helping you out. We'd like to opt you in to our pre-emptive ordering system, so we can help you forget those small essentials. We've included some complementary, ripe, seedless avocados less than 1 day from the tree they were picked from as a sample of the power this feature can offer; this freshness can't be bought in shops."

T+2 "We've opted you in to our pre-emptive ordering system, where we will send you those daily essentials and special seasonal must-haves. There is no commitment. If we ever send you some thing you don't feel you need, we'll happily take it back at no charge and no effort from you."

There is definitely a business model there.

I predict that soon there will be Dash Button [0] like devices embedded in packaging (and/or appliances) so that they can estimate when you are likely to run out of something. First thing you know is more detergent arrives at your door and when you check the existing pack you find that you are indeed running low.

[0] https://www.amazon.com/oc/dash-button

How about distributed/crowd-sourced warehousing?

"We sent you a box of (commonly used item) because we though you might be out. Don't need it? Hold onto it and we'll credit your account $2 if you'll drop it off at a neighbor's house when they order it. Otherwise, let us know and we'll pick it up."

Or just make this process opt-in and let your customers volunteer to make some Amazon cash.

Amazon Prime Now delivers within 1 hour, from early morning until midnight.