Well, if there's one company on Earth that's both incentivized to find an algorithm to efficient pack stuff into their shipping bins and also well-financed enough to actually figure out a good linear or quadratic-time algorithm to do so, it's definitely Amazon.
And once they do so they'll have solved two big problems! :)
They might have the ability to do so. The motivation? Well let me put it this way: I tried Amazon’s grocery delivery service, and stopped using it because everything—everything—kept arriving in its own individual bag regardless of whether it made any sense, so it was just a bunch of bags I had to carry upstairs. That bags also had no handles.
So they were optimizing for something, but it definitely wasn’t packaging efficiency.
Bin packing is theoretically NP Hard but practically solved all the time on real world datasets.
I see what you did there. Touché.
As someone who worked on logistics optimization algorithms for Amazon, I’ll just say that the one thing Amazon did best was have clueless upper management continuously make poor strategic decisions that continuously nullified all of their improvements from optimization.