# The Idea Behind Overselling Flights Is Fine, When Executed Properly

The recent United Airlines debacle shows the worst side of overselling flights. There's the grossly oversold flights to begin with, the complete refusal to entertain any thought of the airline taking a hit as a result of its stuff-up, and then the heinous communications afterwards. But it doesn't have to be that way. There's a smart way to do it, and it's a method that can benefit many other businesses as well.

What I'm talking about is very close to six sigma quality control, which the above video explains. If you can measure the demand and quality of your product, you can make some very accurate predictions and processes for quality control.

Scott E. Page lays out a good example in this video, in which the scenario of overselling a flight is used. Let's say you've been selling exactly as many tickets as your planes have capacity, and you've measured that on average, around 90% of people actually show up for the flight. If this is reliable, it would in theory be okay to oversell flights within a certain range.

In order to get that range, for the set of data you're dealing with, you'll need the mean and the standard deviation. That'll give you a standard bell curve:

Image: Wikipedia

For this example we're going to say that while our planes can hold 380 people, usually 90% show up, so we'll sell 400 tickets. That's a mean of 360 per flight, and there's a standard deviation of 6. (Depending on your data, using the mean absolute deviation may be more reliable)

If there's a normal distribution, then each standard deviation that you move away from the mean will cover 34.1% of occurrences. So if we plan for a range with one standard deviation (in either direction), we account for 68.27% of occurrences. That still leaves 31.73% of instances where we have customers pissed off because they've been bumped from their flight. That's a bit too high, so let's extend our range.

If we plan for a range of two standard deviations, that covers us 95.45% of the time. And if we plan for a range of three standard deviations, that covers us 99.73% of the time. If we plan for a range of four standard deviations, we're covered in 99.994% of instances:

Standard deviations from mean Percentage covered
1 68.27%
2 95.45%
3 99.73%
4 99.994%

So really, it's about what range your comfortable with. In our airline example, customers will expect to be compensated for being bumped, but that cost is easily covered by the process of overselling flights. In a different business, perhaps the consequences of being less than perfect would be severe, and a tighter range would be necessary.

This process does assume a normal distribution, and that each actor is independent, and one person's decision won't affect other peoples' decisions — which might not be entirely true, depending on the nature of your business. In our plane example, there might be families flying together who will obviously make decisions as a group. There may also be weather conditions that cause large groups of people to make a decision to stay home. You can adapt the model to suit your needs.

You can read more about this process here.

Obviously, where airlines like United go wrong is in how much they oversell flights, and of course, how they deal with it afterwards. But when customer satisfaction is a priority, it can be a very useful logistics tool.

And of course, although our example dealt with customer demand, this method can be used for all sorts of quality control. It can even be used backwards, as the above video shows by first working out what range of quality is acceptable in making metal pipes, then using that to find an acceptable standard deviation for production.

## Comments

They just need to incentivise voluntarily leaving the plane. Put them on the next flight first class, give them a free flight, something to make up for the huge, uncomfortable inconvenience caused that isn't even the traveler's fault.

Yeah, should be illegal. They're selling a service they can't provide. In the example above, if they're selling 400 tickets, for a 380 seat flight, they'll get paid for 400 tickets no matter what, due to the horrendous refund policies of airlines. If they want to "oversell" flights, they need to be forced to offer no questions asked full refunds (including all fees) up to a certain point before the flight.

Except that you aren't actually buying a seat on THAT flight... you're buying a ticket which, at the airlines discretion, is exchangeable at the time of check-in for the right to fly on your desired flight.

This is the same case with all forms of ticketed transport (from my understanding, based on the legal framework behind airline travel in australia) across the world.

If airlines, cruise boats, bullet trains and other transport systems with high overheads etc don't make these kinds of business decisions, the only way to continue to be viable and able to expand routes and services etc is to raise prices to make up for potentially unsold seats... would you really prefer that?

No, you absolutely are buying a seat on that flight. If you were just buying a seat on a random flight, you'd just run it like a bus stop, show up with your ticket and get in queue. But it's not run like that, you buy a ticket to specific flight.

Unsold seats will always be a problem, overselling seats is money grabbing. If the flights aren't profitable with the current structure, they need to raise prices, not sell services they can't provide.

Yay, a stats article: will get me in every time! Nice analysis, but I wonder if the Poisson distribution would be more suitable than the Gaussian; Poisson is more reflective of the statistical character of passenger presentations, I would have thought.

The above also does not take into account the chain of reaction from bumping people to other flights (which are already over booked).