Why do airlines sell too many tickets? - Nina Klietsch

譯者: Helen Chang 審譯者: Adrienne Lin

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

你可曾在候診室枯等數小時

despite having an appointment at a specific time?

儘管早已預約指定看診的時間？

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

訂了房，但旅店以客滿為由 而拒絕你住宿？

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

買了票，卻無法登機？

These are all symptoms of overbooking,

這些都是「超額預定」的症狀

a practice where businesses and institutions

亦即商家或機構超賣的行為

sell or book more than their full capacity.

While often infuriating for the customer,

儘管這行為常常激怒客戶

overbooking happens because it increases profits

超賣往往能增加收益

while also letting businesses optimize their resources.

讓商家更有效地運用資源

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

明知不是所有的人都會準時赴約 看醫生、投宿旅店或搭機

reservations,

and flights,

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

所以儘管額滿，仍釋出額外預定名額

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

航空公司是最典型的例子， 部份因這種情況頻繁發生

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

每年約五萬名乘客 因超售機票而無法登機

That figure comes at little surprise to the airlines themselves,

航空公司對此數字一點也不意外

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

因為他們用統計數字 來決定要賣多少機票

It's a delicate operation.

這是個精準的操作

Sell too few, and they're wasting seats.

賣少了，浪費座位

Sell too many, and they pay penalties -

賣多了，可能要付出代價

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

補償金，免費機票、住宿 和惱怒的客戶

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

這是個簡化了的計算方法

Airlines have collected years worth of information

航空公司累計了多年的資料

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

知道誰會、誰不會準時出現 在哪些航班的登機門

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

例如，他們會知道某個特定航線

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

旅客有 90% 的機率會準時出現

For the sake of simplicity,

為了簡化運算

we'll assume that every customer is traveling individually

我們假設每個乘客都獨自旅行

rather than as families or groups.

沒攜家帶眷，也沒參團

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

如果航班有 180 個座位 賣出 180 張機票

the most likely result is that 162 passengers will board.

結果最可能是 162 個乘客登機

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

當然，登機人數可能多於或少於此數

or fewer.

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

每個數值出現的機率

a binomial distribution,

呈「二項分佈」

which peaks at the most likely outcome.

機率最高處是最可能出現的人數

Now let's look at the revenue.

現在看收益

The airline makes money from each ticket buyer

航空公司收取每個乘客的機票錢

and loses money for each person who gets bumped.

但為每個被擠下飛機的乘客花錢

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

假設每張機票二百五十元， 不能改為較晚的航班

And the cost of bumping a passenger is $800.

為每個被擠下飛機的乘客花八百元

These numbers are just for the sake of example.

這些只是舉例的數字

Actual amounts vary considerably.

真正的數字各異

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

所以若不超賣，賺四萬五千元

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

超賣十五張，且至少十五人未出現

you make $48,750.

賺得 48,750 元

That's the best case.

這是最好的情況

In the worst case, everyone shows up.

最壞的情況，每個人都出現

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

十五名乘客不幸被擠下飛機， 收益只餘 36,750 元

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

比當初只賣出 180 張票的收益更少

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

但重要的不只是 每個情況的收益多好或多差

but how likely it is to happen.

而是多容易發生

So how likely is each scenario?

每個情況發生的機率是多少？

We can find out by using the binomial distribution.

可以用二項分佈得到答案

In this example, the probability of exactly 195 passengers boarding

就此例而言

恰好195 個乘客出現的機率

is almost 0%.

接近零

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

恰好 184 個乘客 出現的機率為 1.11%

以此類推

Multiply these probabilities by the revenue for each case,

這些機率乘以各個情況的收益

add them all up,

加總起來

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

用賣出 195 張票的進帳 減去那個總額

and you get the expected revenue for selling 195 tickets.

就得到賣了 195 張票的 期望收益值

By repeating this calculation for various numbers of extra tickets,

依相同的方法計算 每種超賣機票的期望收益值

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

航空公司就能找出 可能得到最大收益值的方案

In this example, that's 198 tickets,

本例是賣 198 張票

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

航空公司可能獲益 48,774 元

almost 4,000 more than without overbooking.

比完全不超賣，多了將近四千元

And that's just for one flight.

那僅是一航班而已

Multiply that by a million flights per airline per year,

乘以每一航空公司每年的百萬次航班

and overbooking adds up fast.

超賣肯定急速地聚少成多

Of course, the actual calculation is much more complicated.

當然，實際的運算要複雜得多

Airlines apply many factors to create even more accurate models.

航空公司會加入其他因素 以得出更精確的模型

But should they?

但是他們應該這樣做嗎？

Some argue that overbooking is unethical.

有些人主張超賣是不道德的

You're charging two people for the same resource.

以同一資源向兩個人收費

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

當然，如果你百分之百確定 有人將會缺席

it's fine to sell their seat.

賣掉他們的座位無妨

But what if you're only 95% sure?

但是倘若你只有 95% 的把握呢？

75%?

75% 呢？

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

可有一個分辨不道德與務實的數值呢？