Why do airlines sell too many tickets? - Nina Klietsch
Have you ever sat in a doctor's office
for hours despite having
an appointment at a specific time,
has the hotel turned down your reservation
because it's full?
Or have you been bumped off a
flight that you paid for?
These are all symptoms of overbooking,
a practice where businesses
and institutions sell
or book more than their full capacity.
While often infuriating for the customer,
overbooking happens because it increases
profits while also letting businesses
optimize their resources. They know that
not everyone will show up to their
appointments, reservations and flights,
so they make more available than
they actually have to offer.
Airlines are the classical example,
partially because it happens so often,
about 50000 people get bumped
off their flights each year.
That figure comes at little surprise
to the airlines themselves,
which used statistics to determine
exactly how many tickets to sell.
It's a delicate operation, sell too
few and they're wasting seats,
sell too many and they pay penalties,
money, free flights,
hotel stays and annoyed customers.
So here's a simplified version of
how their calculations work.
Airlines have collected years worth
of information about who does
and doesn't show up for certain flights.
They know, for example, that
on a particular route,
the probability that each individual
customer will show up
on time is 90 percent. For
the sake of simplicity,
will assume that every customer is
traveling individually rather than
as families or groups, then if there
are 180 seats on the plane
and they sell 180 tickets,
the most likely result is that
162 passengers will board.
But of course, you could also end up
with more passengers or fewer.
The probability for each value is given by
what's called a binomial distribution,
which peaks at the most likely outcome.
Now let's look at the revenue.
The airline makes money from each
ticket buyer and loses money
for each person who gets bumped.
Let's say a ticket costs 250 dollars and
isn't exchangeable for a later flight
and the cost of bumping a passenger
is 800 dollars.
These numbers are just for the sake of
example. Actual amounts vary considerably.
So here, if you don't sell any extra
tickets, you make 45000 dollars.
If you sell 15 extras and at least
15 people are no shows,
you make forty eight thousand
seven hundred fifty dollars.
That's the best case. In the worst case,
everyone shows up,
15 unlucky passengers get bumped and
the revenue will only be thirty six
thousand seven hundred fifty dollars,
even less than if you only sold 180
tickets in the first place.
But what matters isn't just how good
or bad a scenario is financially,
but how likely it is to happen. So
how likely is each scenario?
We can find out by using the binomial
distribution in this example,
the probability of exactly 195 passengers
boarding is almost zero percent.
The probability of exactly 184 passengers
boarding is one point one one percent
and so on. Multiply these probabilities
by the revenue for each case,
add them all up and subtract the sum from
the earnings by 195 sold tickets
and you get the expected revenue
for selling 195 tickets.
By repeating this calculation for various
numbers of extra tickets,
the airline can find the one likely to
yield the highest revenue in this example.
That's 198 tickets from which
the airline will probably make forty eight
thousand seven hundred seventy four
dollars, almost 4000 more than
without overbooking.
And that's just for one flight.
Multiply that by a million flights
per airline per year.
And overbooking adds up fast.
Of course, the actual calculation is much
more complicated airlines apply many
factors to create even more accurate
models, but should they?
Some argue that overbooking is unethical.
You're charging two people
for the same resource.
Of course, if you're 100 percent
sure someone won't show up,
it's fine to sell their seat. But what if
you're only 95 percent sure, 75 percent.
Is there a number that separates being
unethical from being practical?
