Question

American Airlines. (AA) is an airline that operates direct, daily flights between Los Angeles (LAX) and London Heathrow (LHR) airports. AA offers only business-class tickets and service on all of its flights. On the LAX-LHR route, AA flies Airbus 320 plane configured to have a capacity of 100 business-class seats.

AA sells tickets on LAX-LHR route at $3000 and offers a generous, 90% “last-minute cancellation” policy. In particular, under such policy, a customer may cancel her flight up to 30 minutes before the departure time and receive back 90% of the $3000 fare she paid. As a result, AA is able to sell many more tickets than its plane capacity. The downside is that customers who purchased tickets may not all show up for the flight.

To better manage the profitability of its LAX-LHR route in the presence of last-minute cancellations, AA uses “overbooking,” that involves selling more tickets than 100 seats on its plane. In particular, AA would like to compare two overbooking options: 1) selling T=110 tickets, and 2) selling T=115 tickets. AA is confident that, given the moderate business-class fare it charges and a generous cancellation policy it offers, it can always sell those numbers of tickets.

The sequence of events in the presence of overbooking is as follows:

·Tickets are sold to T potential passengers at the price of $3000 each

·At about 30 minutes prior to departure, the number of customers who actually show up for the flight, A, is revealed (0≤A≤T) and the refund of $2700 is paid to each of T-A customers who did not show up

·If A≤ 100, the plane takes off with A customers on board

·If A>100, the airline asks for A-100 volunteers to release their seats and to accept alternative flight arrangements, for additional compensation. As a result of this process, the airline pays to each of A-100 volunteers the compensation of $5000, and the plane takes off with 100 customers on board.

Thus, the revenue that AA earns for a particular flight depends on the values of T and A, and consists of three components: the initial revenue from selling tickets minus the refund, if any, paid for last-minute cancellations, and minus the additional compensation, if any, paid to customers asked to release their seats.

1) Suppose that AA decides to use Option 1 (i.e., sell T=110) tickets, and the number of customers who show up for the flight is 100. What is the revenue that AA will earn for this flight, in $? Round your answer to the closest integer value.

2) Suppose that AA decides to use Option 2 (i.e., sell T=115) tickets, and the number of customers who show up for the flight is 105. What is the revenue that AA will earn for this flight, in $? Round your answer to the closest integer value.

3) Zero Management is a business analyst working for AA who was assigned a task of comparing the two overbooking options described above. Zero has decided to design a simulation model that assumes that each of T customers who bought tickets has a probability of 0.9 of actually showing up for the flight, and that each customer makes a decision to show up for the flight independently of other customers. A statistician working for AA explained to Zero that, under these assumptions, the number of customers who actually show up for the flight, A, is a binomial random variable that can take integer values 0,1,2,… T, and that has the expected value of 0.9*T.

Suppose that the AA decides to use Option 1 (T=110). Let A be the number of customers who actually show up for the flight under this option. The algebraic expression for the revenue that AA earns for this flight, in $, is

a)   330,000 – 2,700*(100-A) – 5,000*IF(A<100, 0, A-100)

b)  330,000 – 2,700*(110-A) – 5,000*IF(A<110, 0, A-110)

c)   330,000 – 2,700*(110-A) – 5,000*IF(A<100, 0, A-100)

d)  330,000 – 2,700*(100-A) – 5,000*IF(A<110, 0, A-110)

4) Consider Option 1 (T=110). If it is possible for A to take integer values 0,1,2,…,110, what is the maximum possible revenue, in $, that AA can earn for a flight? Choose the closest value.

a)   330,000

b)  303,000

c)   300,000

d)  280,000

e)   270,600

5) Consider Option 1 (T=110). If it is possible for A to take integer values 0,1,2,…,110, what is the minimum possible revenue that AA can earn for a flight? Choose the closest value.

a)   303,000

b)  280,000

c)   270,600

d)  33,000

e)   0

Answer 1

Question 1)

So if T =110 the flight is overbooked

100 customers showed up for the flight

so 10 customers did not show up, so AA has to pay 2700 *10 = 27000 dollars

110 tickets were sold, so money gained = 3000 * 110 = 330000

So net revenue = 330000 - 27000 = 303000

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Question 2)

Suppose American Airlines sells 115 tickets and 105 people show up

So for no show, i.e for 10 people so AA has to pay 2700 *10 = 27000 dollars

out of 105 people who showed up, 5 are overbooked, so AA has to pay 5000 * 5 = 25000 dollars

115 tickets were originally sold, so money gained = 115 * 3000 = 345000

So net revenue = 345000-25000-27000 = 293000

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Question 3)

No show refund = 2700 * (T-A) so and T = 110, so this rules out option a and d.

the answer is either b or c

now 5000 is paid when A is greater than 100 and is paid to (A-100), so it should be 5000 *(A-100) , A cannot be greater than T,

So the answer has to be option c

330,000 – 2,700*(110-A) – 5,000*IF(A<100, 0, A-100)

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Question 4)

We know that

Revenue = 330,000 – 2,700*(110-A) – 5,000*IF(A<100, 0, A-100)

this will be highest when A = 100 and the value will be 303000

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