Why do airlines sell too many tickets? - Nina Klietsch

翻译人员: Shelly 莹嫣 Yao 姚 校对人员: Wenzi Yang

Have you ever sat in a doctor's office for hours

你有没有曾经等医生几个小时看诊的经历？

despite having an appointment at a specific time?

尽管你有提前预约特定的时间？

Has a hotel turned down your reservation because it's full?

你有没有经历过被酒店拒之门外因为客满？

Or have you been bumped off a flight that you paid for?

或者你有没有经历过被航空公司拒载尽管你买了票？

These are all symptoms of overbooking,

这些都是超额预定的现象，

a practice where businesses and institutions

一个公司或者机构

sell or book more than their full capacity.

卖出或者预定大于他们容量的行为。

While often infuriating for the customer,

尽管这行为使客户很愤怒，

overbooking happens because it increases profits

超额预定的存在因为它可以增大利益

while also letting businesses optimize their resources.

这还使公司更好的优化资源。

They know that not everyone will show up to their appointments,

它们知道不是所有的客户都会出现，

reservations,

预约的时间，

and flights,

和预约的航班，

so they make more available than they actually have to offer.

所以它们会提供比它们实际容量更多的空位。

Airlines are the classical example, partially because it happens so often.

航空公司就是一个经典案例，一部分因为它发生地太过频繁了。

About 50,000 people get bumped off their flights each year.

每年大约有50，000人被拒载。

That figure comes at little surprise to the airlines themselves,

这个数字让航空公司也大吃一惊，

which use statistics to determine exactly how many tickets to sell.

因为它们有利用统计数据去分析售票情况。

It's a delicate operation.

这是一个精准的运算。

Sell too few, and they're wasting seats.

卖了少了，它们浪费了空位。

Sell too many, and they pay penalties -

卖了多了，它们有会遭到惩罚。

money, free flights, hotel stays, and annoyed customers.

钱，免费的机票，酒店和恼怒的客户。

So here's a simplified version of how their calculations work.

这里呢，有一个简化版的公式，告诉你这个计算是如何运行的。

Airlines have collected years worth of information

航空公司累计了多年的数据和信息

about who does and doesn't show up for certain flights.

关于谁会或者不会出现在一个特定的航班。

They know, for example, that on a particular route,

举个例子，它们知道在一个特定的航线，

the probability that each individual customer will show up on time is 90%.

每一个客户的按时出现率是90%

For the sake of simplicity,

为了简化运算

we'll assume that every customer is traveling individually

我们假设每个人都在独自一人旅行

rather than as families or groups.

并没有家人或者团队

Then, if there are 180 seats on the plane and they sell 180 tickets,

那么，如果航班有180个空位，它们就会卖180张机票

the most likely result is that 162 passengers will board.

结果会是162个乘客出现在飞机上

But, of course, you could also end up with more passengers,

当然，

or fewer.

也有可能更多或者更少的乘客出现

The probability for each value is given by what's called

每个数值出现的几率是通过

a binomial distribution,

二项分布得出的

which peaks at the most likely outcome.

在最有可能的情况下达到最高点

Now let's look at the revenue.

现在我们来看一下收益

The airline makes money from each ticket buyer

航空公司在每个乘客身上赚钱，

and loses money for each person who gets bumped.

在被拒载的乘客上损失钱

Let's say a ticket costs $250 and isn't exchangeable for a later flight.

如果每张票买$250美元，并且不能改签

And the cost of bumping a passenger is $800.

拒载一位乘客会花费航空公司$800

These numbers are just for the sake of example.

这些数字只是为了举例子而已

Actual amounts vary considerably.

真正的数字根据情况会有不同

So here, if you don't sell any extra tickets, you make $45,000.

所以，如果你不卖出更多的票子，你会赚$45,000

If you sell 15 extras and at least 15 people are no shows,

如果你多卖15张票，并且这些乘客都没有出现

you make $48,750.

你会赚$48,750

That's the best case.

这会是最好的情况

In the worst case, everyone shows up.

最坏的情况，每个人都出现

15 unlucky passengers get bumped, and the revenue will only be $36,750,

15个不幸的乘客会被拒载，收益也只会是$36,750

even less than if you only sold 180 tickets in the first place.

比卖出180张票要来的更少

But what matters isn't just how good or bad a scenario is financially,

但是重要的并不只是财政上的好与坏

but how likely it is to happen.

重要的是这有多么容易发生

So how likely is each scenario?

每个情况发生的几率是多少？

We can find out by using the binomial distribution.

我们可以通过使用二项分布来得出答案

In this example, the probability of exactly 195 passengers boarding

在这个例子中，正好有195个乘客出现的几率

is almost 0%.

大约为0％。

The probability of exactly 184 passengers boarding is 1.11%, and so on.

184个乘客出现的几率为1.11%，以此类推。

Multiply these probabilities by the revenue for each case,

用这些几率乘以每个情况下的收益，

add them all up,

然后把它们加起来，

and subtract the sum from the earnings by 195 sold tickets,

再减去卖出195张票的收益，

and you get the expected revenue for selling 195 tickets.

你会得出卖出195张票的预计收益。

By repeating this calculation for various numbers of extra tickets,

在多卖出的票上重复使用这个计算，

the airline can find the one likely to yield the highest revenue.

航空公司可以找出一个最后可能得到最大收益的方案。

In this example, that's 198 tickets,

在这个例子中，为卖198张票，

from which the airline will probably make $48,774,

航空公司可以以此得到$48,774的收益，

almost 4,000 more than without overbooking.

比没有超额预定多赚了$4,000。

And that's just for one flight.

这仅仅是一架航班而已。

Multiply that by a million flights per airline per year,

用这个数字乘以每个航空公司每年上百万的航班，

and overbooking adds up fast.

超额预定就聚少成多了。

Of course, the actual calculation is much more complicated.

当然，实际的运算要逼着复杂很多。

Airlines apply many factors to create even more accurate models.

为了得出更精确的模型，航空公司会增加其他因素。

But should they?

但是它们这样做应该吗？

Some argue that overbooking is unethical.

有些人主张超额预定是不道德的。

You're charging two people for the same resource.

你用同一个东西在两个人身上收取了的费用。

Of course, if you're 100% sure someone won't show up,

当然，你如果能百分百确定有人不会出现，

it's fine to sell their seat.

出售他们的座位也是允许的。

But what if you're only 95% sure?

但是如果你只是95%确定呢？

75%?

75%？

Is there a number that separates being unethical from being practical?

能否有一个数字能用来区分不道德行为和面对实际？