It might sound incongruous but mathematical theory seems to hold the key to the success or failure of a fledgling industry: air-taxis.
John Gapper writes in the FT about the launch of new air-taxi businesses in the US. The aim of these businesses is to ferry a small number of passengers (6 or so), point-to-point at prices lower than typical corporate jets. He comments in this context:
What if that world were democratised and more people, including sales representatives or executives of small businesses, had their own taxi service of the air? They, too, could fly directly from small airports close to their homes to others near their destinations. If such a service were affordable, it would save a lot of discomfort and wasted time.
But there are a number of obstacles, the most significant of them, it seems to me, being the need to have large numbers of air-taxis scooting around from place to place. The fundamental (regulatory) requirement for operating an air-taxi service is that flights cannot operate according to a fixed schedule. This means that profitably operating a fleet of jets hopping from point to point can be a fearsome exercise in scheduling. This is where the math comes in. One company has even hired "a group of mathematicians from the Santa Fe Institute", according to John Gapper.
By the way, seeing the word "democratised" in the article got me all excited about how big the potential market could be for air-taxis. I got the impression that anyone and his dog could hop into one and go for a jaunt. Not really, in actuality.
Air-taxis are a democratising business in the sense that they offer a premium service (point-to-point, personalised) to larger numbers of people than before. But tickets aren't cheap -- one company expects to charge on average "about twice a flexible economy fare for a similar distance". That's still a pretty good deal for those in the market.
Link: John Gapper: Munificent men in their flying taxis (subscription required)