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I would pay generously to take a guided tour of Amazon's fulfilment centre. I imagine it to be a hive of activity. Most of us take next day delivery for granted now, but when taking into account the volume Amazon must process every day, I find it fascinating. Even more so when you take into consideration their same day (evening delivery) service.
I'd guess that next-day or same-day delivery is simply a consequence of efficient HR and not a goal in it self.

If fulfilment takes n minutes on average pr. order, they need n x number of orders staff-time. Unless they execute the order immediately after its placed (or at least all stocks are available), orders will pile up. The efficiency is simply to match staff with order, and with a large volume of orders and a large staff, that's quite simple to pull off. With rolling shifts, you can ask one shift to stay on for 10-15 minutes and instantly have 10s of hours of added capacity.

I work for Amazon, this post is my own opinion, not of my employer, yadi yada. I obviously can't say much, but I just have to say it really is not as simple as you're making it sound ;) It goes much, much, much further than just having X people in a warehouse :P
Right.

Initially you're trying to optimize the path for X people. So to get X items which are distributed in a given way, you're trying to have each person take the shortest path possible.

However, based on orders, you want to optimize the distribution of items in the warehouse to further shorten the paths. Granted, that distribution could be biased wildly based on all sorts of factors (i.e. seasonal activity).

Fun problem to say the least. :)

I own and run two smallish ( ~ $1 mill/yr ; ~ $0.5 mill/yr revenue) ecommerce stores ( http://smartflix.com and http://heavyink.com ) and I bought a few textbooks books on warehouse layout and design.

There really wasn't a lot in there that was applicable to me, but I bet that (a) the Amazon folks have all read these books, and (b) they could write much, much better ones if they wanted to spill some of their trade secrets!

Well done. How did you scale up smartflix? That seems like a very challenging problem. Did you need to spend a great deal of money to create a useful initial stock of DVDs ?
Not all at once, but yes.
Now we know where the Ark of the Covenant really is.
So much wasted vertical space?