Using Science to Cut Boarding Time

During my 25 year career at Delta Air Lines, I watched the boarding process thousands of times. Even before I began my Lean and Six Sigma journey, I always knew there was a ‘better way’ to board an airliner. But I never got the opportunity to apply Lean or Six Sigma to the boarding process. The attached re-post is an article about how one physicist and his idea of how to speed the boarding. I don’t know if his ideas could work in the real world, but I recommend that everyone in my extended Delta Family check out this video… it’s pretty cool.

Bob H

Physicist cuts plane boarding time in half

August 30, 2011 3:27 PM PDT
Passenger jets seem designed to waste time, what with people trying to stuff oversized carry-on bags into undersized luggage bins, aisles clogged with people, and a billion other factors that delay your flight.

A few years ago, Fermilab astrophysicist Jason Steffen observed this while flying to a conference and got to thinking: is there a way to have passengers board a plane more efficiently?

Steffen considered various methods, such as boarding people in blocks, at random, and in window seats first. He set up a model using an algorithm based on the Monte Carlo optimization method used in statistics and mathematics.

He found that the most efficient boarding method is to board alternate rows at a time, beginning with the window seats on one side, then the other, minimizing aisle interference. The window seats are followed by alternate rows of middle seats, then aisle seats. He also found that boarding at random is faster that boarding by blocks.

The results of his study were published in the Journal of Air Transport Management in 2008, with Steffen claiming the airline industry could save massive sums with more efficient boarding.

Needless to say, we’re still boarding by blocks. Steffen’s research, though, was recently highlighted on an online video show called This vs. That.

Steffen and the show’s producer used a mock 757 fuselage section on a sound stage, recruited 72 mock passengers, and tried five boarding methods. Shown in the vid below, the “Steffen method” of boarding alternate rows reduced overall boarding time by about half.

“This savings could be as much as $110,000,000 annually per carrier–well over a billion dollars for the industry–and likely could be more given the parallel nature of the boarding process,” Steffen writes in a recent follow-up paper. “Indeed, a test with a longer aircraft may show surprising results in this regard.”

Read more:

This is from Jason Steffen’s home page.

I had been thinking about this problem for two or three years and decided that I needed to either satisfy my curiosity or forget about it. I was able to squeeze two publications out of this work. The first article is on the optimal method to board passengers—based upon a simple, but (in my opinion) plausible, model. This article appeared in the Journal of Air Transport Management (the choice of journal was because I recognized the publisher, and it fortunately turned out to be a leading journal in the industry). The upshot is that the optimal method is one that parallelizes the boarding process rather than serializes it (like most carriers have done in the past). People standing in the aisle of the airplane are just standing in line. Loading back to front just moves the line inside the plane, but is not significantly faster than loading from the front to the back. This method has as many people as possible using the aisleway to store their luggage, allowing many more people to simultaneously prepare to sit.

An example passenger boarding order that is a member of the class of optimal methods.

The second publication was a method to model free-for-all passenger boarding (like Southwest Air) which appeared in the American Journal of Physics. Here, I assigned a potential to each seat based upon the seat preferences of the passengers. Whenever a decision about where to sit needs to be made, a passenger (at some temperature that is a measure of their laidbackness) will make that decision using Boltzmann probabilities. Once they sit down, they don’t move and the partition function is updated. I was pleased to see to see how well the decision making model, airplane boarding model, and the monte carlo reproduced the expected Fermi-Dirac distribution of seating. On the left is an example of the potential for each seat. The center shows the partially filled airplane as a function of increasing temperature. The right image shows the occupancy of the different seats for the same temperatures shown in the center (found with a monte carlo) also plotted are the predicted Fermi-Dirac distributions for these temperatures. Note that since the decision making and passenger boarding models ultimately result in a microcanonical ensemble of passenger states, the chemical potential is determined by the number of passengers and their energies and not by a chemical potential of a passenger exchanging reservoir (as in the grand canonical ensemble).

I was quite surprised about the media attention that this work received. Indeed, it was interesting to see the gestation period between posting the first paper on the arXiv and watching it appear on blogs and in other media outlets. It started on Cosmic Variance (thanks Julianne), and within a few hours appeared on a Cornell University economics class blog talking about Braess’ Paradox (I think it was an econ class, I can’t find the post any more). My first phone call from a reporter was at about day four. Interest peaked between days 10 and 14 with articles having appeared on,, New Scientist, Nature news, Slashdot, a bunch of news websites (CNN, ABC, etc.) and both foreign (from Germany to Korea) and domestic newspapers (including my hometown Davis County Clipper). My first radio interview was with the BBC which spread to NPR (see below), a Canadian news agency, and some radio shows in Ireland and Australia—there were others, I should have kept better records but unfortunately didn’t. Another interesting thing was how I became a nuclear physicist, an atomic physicist, and a rocket scientist as the reporting went to second and third-hand sources. I’m sure someone has done a study on how news stories evolve during their lifetimes, it was interesting to watch it happen in real-time. article article
Nature News article
Radio interview on NPR’s “All Things Considered”.

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