>I would think that Walmart probably has a competitive advantage in most logistical areas. They've been moving goods across the country (and world) for longer than Amazon has been a company.

Walmart does not have a competitive advantage in logistical areas. Have a look at a youtube video of what happens in an Amazon FC. Amazon does not simply box packages and ship them.

I would say Amazon is implementing the physical manifestation of algorithms onto physical goods, but that only scratches the surface of the complexity required to optimize the entire chain from customer desire to fulfillment.