Additional Math Pages & Resources

Monday, June 27, 2011

The Fastest Way to Board, Part I

The point of this blog is to explore ways that adults can use the math they learned in elementary school. Today we take on an irritating process most of us have experienced - boarding a commercial aircraft. My main qualification to tackle this complex subject is personally accumulating 3 million frequent flier miles, including 2,286,450 miles on American Airlines alone.

What's the best way to do the boarding process? Can Math Help? That is the question.

Here are some options:
  1. No assigned seats - everyone rushes for the seat they want
  2. No assigned seats - order imposed outside the plane and freedom of selection inside
  3. All seats assigned - board in random sequence
  4. All seats assigned - board from back of the plane to the front
  5. All seats assigned - board in small groups alternating at back, then front, then back, then front.
  6. All seats assigned - board the window passengers first, then center seat, then aisle
  7. All seats assigned - board one side of the plane first, then the other
  8. All seats assigned - board using "flying carpet" method (more on this later)
Here are the goals:
  1. First and business class offered priority
  2. Frequent fliers offered next priority
  3. Families with children, seniors, wheelchairs, etc. given extra time
  4. All passengers moderately satisfied
  5. Plane loaded faster ($30-75 per minute value to airlines)
With about 28,000 flights per day in the US, only 5 minutes saved boarding each flight would decrease airline costs $4.2-10.5 million per day and result in less aggravation to 3.5 million passengers. Multiply that by a year, and we're talking real money - billions! A real incentive to improve this tangle:
From Speeding up the airplane boarding process by using pre-boarding areas by Albert Steiner and Michel Philipp
Sadly, here are some problems:
  1. Crowded planes increase the boarding time but full flights are more profitable for airlines
  2. Less carry-on luggage decreases boarding times and may increase revenue (airlines like this) but carry-ons save passengers time and money (passengers like this)
  3. Boarding times are influenced by other airport processes - security checks, shopping, cabin cleaning, etc. which impact passenger boarding
  4. The aircraft itself influences boarding due to number of doors, number of aisles, aisle width, number of seats per row, bathroom locations, overhead bin sizes, etc.
  5. Passengers ignore these methods and "do their own thing" at least 10% of the time
  6. Weather plays an unpredictable role as the number of coats, hats, etc. impact the loading times
  7. The human factor - flight attendants, gate agents and passengers all impact boarding times by helping or hindering
  8. Although more than half of passengers travel alone, each plane has roughly 20 parties of 2 and 9 parties of 3 passengers sitting together (rarely are there larger groups).
A quandary arises as we notice there are a few passengers who willfully disregard the assigned process. These people (a) please themselves, (b) usually speed the boarding process for everyone, but (c) irritate other passengers. Common sense ("no one's going now") and selfishness ("so I'm going now") work together to overcome inefficient procedures and baffle the people doing simulations.

So how do we find the best method?
  1. We can do observations: watch people, film them and time them
  2. We can do simulations: create software or mechanical simulators to run through scenarios
  3. Trial runs with real agents and passengers
  4. We can think hard, then apply trial and error and develop our own method.

More tomorrow!