See http://www.wolframalpha.com/input/?i=log2%28one+quintillion%....

The best way I could think of to generate lots of variables is a random forest classifier, which is an ensemble of (say) thousands of trees. Each tree constructs a lot of variables at each node, so maybe you'd have (stretching here) hundreds of thousands to perhaps millions of variables. But 1e6 << 1e18.

Maybe they're counting each pixel of some remote sensing image of orange groves? Bullshit again, that would have to be a 1e9 x 1e9 pixel image. I'd believe it from NGA (http://en.wikipedia.org/wiki/National_Geospatial-Intelligenc...), but not from Coke.

If there's a shred of truth to it, they're using some dodgy mechanism to increase the variable count.

So all this stuff about classifiers is off base. This isn't a predictive model -- it's a math program.

I don't know how they got that quintillion number. Could be that many "variations" instead. But the dimensions are things like time, varietals, locations, what you're gonna store/blend, that kind of thing. You end up with decision variables that are indexed in multiple dimensions and that creates the variable explosion they're alluding to.

CPLEX is awesome at handling huge amounts of decision variables so long as the problem stays mixed-integer, and that's what this is.