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  • Have you ever sat in a doctor's office for hours despite having an appointment at a specific time?


  • Has a 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 50,000 people get bumped off their flights each year.


  • That figure comes at little surprise to the airlines themselves, which use 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 penaltiesmoney, 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%.

    舉例來說,他們知道某一特定航線的單一旅客準時出現機率是 90%。

  • For the sake of simplicity, we'll 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.

    那麼,如果飛機上有 180 個座位,他們全數賣光,最可能的結果是有 162 位乘客登機。

  • 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 and isn't exchangeable for a later flight, and the cost of bumping a passenger is $800.

    我們假設一張機票價格是 250 美元,且不可更換至後續航班,而讓一名乘客延遲班機的成本是 800 美元。

  • 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 $45,000.

    在這裡可以看到,如果不超賣機票,能賺 45,000 美元。

  • If you sell 15 extras, and at least 15 people are no-shows, you make $48,750.

    如果超賣 15 張票,且至少有 15 位乘客未出現,你能賺 48,750 美元。

  • That's the best case.


  • In the worst case, everyone shows up.


  • 15 unlucky passengers get bumped, and the revenue will only be $36,750, even less than if you only sold 180 tickets in the first place.

    15 位不幸的乘客被延班機,營收只有 36,750 美元,甚至比當初如果只賣 180 張還少。

  • 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 0%.

    在這個例子中,195 位乘客全數登機的機率接近 0%。

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

    184 位乘客登機的機率為 1.11%,以此類推。

  • 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.

    將每一個可能結果的營收乘上機率,把它們相加然後扣掉 195 張票的收入,就能得到販賣 195 張票的預期營收。

  • 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 $48,774, almost 4,000 more than without overbooking.

    在這個案例中,198 張是最理想的數字,航空公司能從中獲取 48,774美元,比起不超賣多了近 4,000 美元。

  • 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% sure someone won't show up, it's fine to sell their seat.


  • But what if you're only 95% sure?

    但如果你只有 95% 的確定性呢?

  • 75%?

    或 75%?

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


Have you ever sat in a doctor's office for hours despite having an appointment at a specific time?


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B1 中級 中文 美國腔 TED-Ed 航空 乘客 營收 航班 機率

【TED-Ed】為什麼航空公司要超賣機位? (Why do airlines sell too many tickets?)

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    Darren 發佈於 2020 年 10 月 18 日