Another proposed solution to the airplane boarding problem:

[Physicist Jason] Steffen found that the worst method for boarding a plane is boarding from the front to the back, since passengers have to wait and step over each other to get to their seats. ...Quite unexpectedly, then, Steffen found that the common back-to-front boarding method is actually the second worst method possible, only slightly better than boarding front to back.

...Using a combination of a Monte Carlo optimization algorithm and intuition, Steffen determined an optimal boarding method, which could make boarding go 4 to 10 times faster than the worst method, depending on the size of the plane. In the optimal method, passengers would board 10 at a time in every other row (since loading luggage requires about two aisles of space). This way, passengers could always be boarding luggage or sitting in their seats, rather than waiting in the aisle, as in the two previous methods.

However, Steffen also acknowledged that the optimal method might not be practical, since passengers who sit next to each other often travel together, and prefer to board together. He proposed a modified version, where passengers board in blocks of three consecutive seats on one side of the plane in every other row. In this strategy, there would be four boarding groups, with passengers in the same row on the same side boarding together. This method provided a decent middle ground, as it was twice as slow as the optimal method, but twice as fast as the conventional method. Although getting passengers to line up in their correct groups might sound challenging, Steffen noted that Southwest Airlines has been experimenting with having its passengers line up in numerical order -- so the logistics wouldn't be inconceivable.

Steffen also identified several other boarding strategies with results superior to the conventional method. Contrary to our tendency for order, even completely random boarding proved to be a good alternative. In fact, random boarding was nearly as fast as the modified optimal method. Plus, by its very nature, it has the advantage of not requiring airline attendants to organize boarding passengers in any way. And the random result also shows that, when passengers board out of order in the other strategies, the results will still be better than the conventional boarding method.

The main advantage of the alternative boarding methods is that they allow several passengers to load their overhead luggage simultaneously, which Steffen identified as the largest factor in determining boarding time.

The merits of random boarding have been discussed here in this 2006 article.