Additional Math Pages & Resources

Tuesday, June 28, 2011

The Fastest Way to Board, Part II

I'm continuing the topic from yesterday, on using math to find the best way to board an aircraft. I'll start with a quote:

Dr Eitan Bachmat, doing research at Ben- Gurion University said: "What we suggest is that airlines just don't bother too much with annoying their customers and either board randomly or, if they want to do something, let the window people on, then the middle and then the aisle seats. Playing with the rows seems to be futile."

I read a study from Boeing, who wants to sell profitable planes. Since Boeing has aircraft handy, unlike most researchers, they used some and filled them repeatedly with volunteer passengers. Boeing's research indicated that loading times can be improved by:
  • using doors nearer the middle of the aircraft (possible on some jumbos)
  • two doors (ditto but dual jetways are quite rare in airports)
  • two aisles (only on wide-body planes)
  • loading from windows in toward the aisles
The back-to-front method only works best on jumbos (747 types) where two aisles, 40+ rows and lots of room diminish the conflicts.

Boeing says loading rates have slowed from 20 passengers/minute in 1965 to 10 passengers/minute in 2000.  Deplaning has also slowed, from 27 passengers/minute to 17 passengers/minute.

What has caused this massive drop in efficiency over 25 years? Based on what I have read and observed:
  • More carry-on baggage (resulting in more fussing around rather than sitting down)
  • Higher load factors (more crowded planes)
  • Longer planes (uh, Boeing didn't say this)
  • Tighter seating, fatter people, and thinner aisles (politically incorrect observations ...)
  • General lack of attention from passengers (cell phones, cups of coffee, etc.)
I boarded Concorde once, eight years ago. Just over 100 passengers loaded in under 5 minutes. How? No overhead bins to speak of, no carry-on luggage allowed, only 4 seats per aisle and everyone excited and focused on getting in our seats. We used the random method.


 Back to the original question - can we use math to summarize our findings?  Of course we can. Who would believe a blog post without a chart or graph? So here's one I have created, from a research project that compared different boarding methods:

The best result was alternating both seat letters and rows, so no conflicts arise in loading the overhead bins. For example, the gate agent would say:

Row 5 A and Row 7 F
Row 9 A and Row 11 F
Row 13 A and Row 15 F
please board now.

That approach is fastest for people once they are on the plane, but sadly it's very confusing to people in the gate area. So most researchers discard that option. This report recommended either "multiple small groups" or "seat letter groups".

Can you see a consensus appearing? Three of the expert reports suggest the gate agent say something like this:

Now boarding all rows for windows seats only please. Seats A and F only.
then
Now boarding all rows for center seats only B and E and window seats if you haven't already gotten on.
then
Now boarding all rows for aisle seats C and D. Last call.

Yes there are issues with people sitting together, but hey, it's only for a few minutes and you can cheat if you have to - a few defectors might even speed up the process.