Math Modeling Can Get You Kicked Off A Plane

[This is one of a series of posts that explore real world examples of mathematical modeling to help educators better understand its applications. The most important post to read is this one about spies and analysts, which is a context I refer to in each of the posts.]
 
Do you remember reading about the man who was literally dragged off a United Airlines flight in April 2017? One of the questions people had was “Why was he the one they picked?” People speculated that it might have been because of his race or spoken language.

The reality was that, for both better and worse, that had nothing to do with why he was picked. He was picked because United Airlines used mathematical modeling to determine that he was their least profitable customer.
 

Very often people miss their plane flights, so airlines tend to sell more tickets than there are seats on the plane. Usually, no one notices this way in which airlines try to maximize their profits because there almost always are enough empty seats from people who miss their flight. When there aren’t enough seats, then problems happen.

In this case, when United Airlines could not persuade someone to give up their seat, they had to decide which passenger would be forced to leave. Put another way, if you had 201 people for a 200-person flight, how would you choose the one person who would not fly?

Stop and take thirty seconds to think about this. Out of all the available information, what would you want to help you make this decision? This is where the spy component comes in. What I mean is that with mathematical modeling one very important but often underappreciated part is acquiring the data. What data do you need? How are you going to get it? When you’ve got an idea of what data you would use, read on.
 

Realize that United had to go through this same process and in their Contract of Carriage Document it states that “If there are not enough volunteers, other Passengers may be denied boarding involuntarily in accordance with UA’s boarding priority” and then “the priority of all other confirmed passengers may be determined based on a passenger’s fare class, itinerary, status of frequent flyer program membership, and the time in which the passenger presents him/herself for check-in without advanced seat assignment.”

So, out of all the data they could choose from, they picked these as the most important:

• Fare class (coach vs. business vs. first class)
• Itinerary (are there any connecting flights and will this missed flight create a chain reaction of missed flights?)
• Status of frequent flyer program membership (loyal frequent flyers generate more money)
• Check-in time (presumably those who checked in earlier should get priority)

Now with the data chosen, this is where the analysts come in. What are they going to do with all this information? How are they going to manipulate it to create a mathematical model (which could also be called a formula or algorithm) to weigh the variables and decide which customer is the least profitable for them? In other words, if being kicked off a plane made the customer so mad that they never purchased a flight from them again, who would cost United the least amount of money?

I’m definitely not stating that I like their mathematical model, that the practice of overselling flights is sound, or that they handled asking him to leave in a professional manner. I’m just trying to show you an example of how mathematical modeling is used. I want to open up some of the complexities so that we realize that if our job was creating the formula, it wouldn’t be easy.

If this was a stereotypical textbook problem, it might begin by giving the already created formula and a set of data. Then it might ask you to determine which person would not fly. That would not be mathematical modeling though. Creating the actual mathematical model, not using it, is the hardest part.