航空公司的售票营销策略

应用统计学案例3，学时：36小时，案例规模：中

类型：选编来源：Statistics For Business And Economics,David R. Anderson

South-Western Thomson Learning,1998

E stimating the chances of “No shows” and Is Overboo king Worth it? Transamerican Airlines has opened a new daily flight from Chicago to Boise, Idaho. It is so popular that its 75 seats have all been reserved in its first 20 flights Unfortunately, in each flight some of the passengers failed to show up. So that the plane left with some empty seats and lost revenue.

The number of “no shows” varied from 2 on the best flight to 11 on the worst flight. Here are the details:

To reduce the number of empty seats, the airline can sell more than 75 reservations, of course. But that introduces a new risk of overbooking, if more than 75 people show up with reservations. In order to properly balance its risks, the airline needs to estimate the chances of various no shows”. We therefore imagine collecting data for many flights (under similar conditions) so that the relative frequencies would settle down to probabilities p(x). Let us estimate one of these probabilities-for example, the chance of exactly 3 “no shows”, p(3).

a.To estimate this long-run relative frequency p(3). The shortrun relative frequency in the table above is 4/20=0.20. Do you think this estimate is too high, or too low? Why?

b.G raph the relative frequency distribution of X from the table above. Sketch a smooth curve through it-a crude probability of p(3)?

c.For a more refined model, let p denote the proportion of passenger who are “no shows”, Then assume that a flight consists of n=75 randomly chosen passengers. So that X has binomial distribution.

To estimate p. how many passengers were there altogether in the 20flights? And how many “no shows”? So what is your estimate of p?

d.N ow estimate p(3) using the binomial distribution. Graph it alongside you other estimates for comparison.

e.Transamerican therefore planned to “overbook”, making reservations for n=78 passengers. Assuming they form a random sample from the whole population of passengers, what is chance of an overload crisis, that is, more than 75 actually showing up for the flight?

f.Transamerican also considered the riskier plan of making reservations for n=80 passengers. Using the binomial formula, a computer printed out the following schedule of how many passengers would show up (y):

g.T o determine whether the overbooking in b was worth it, various costs have to be considered. The simplest costs to quote are the conceptual losses in revenue, incurred by failing to achieve the opportunity of a plane ideally loaded with exactly y=75 passengers showing up. Called “Opportunity Losses” in management science, they are the same idea as “Opportunity Costs” in economics.

Opportunity Losses:

i.If y<75, each empty seat costs $200 in lost revenue.

ii.If y<75, each extra passenger who gets turned away costs $400, because of a “double your money back” guarantee.

What is the expected opportunity loss (EOL) for booking n=80?

h. What is the EOL for the conservative booking n=75? (Hint, What is the expected number who don,t show? How much does each cost? )

i. Which is the better policy, booking n=75 or n=80? Over the 365 flights in a year, about how much would they gain from using the better policy (instead of the other)?

*j. Using Minitab or similar softwear, verify that the better policy in i is very best of all. (Hint For n=80, use the BINOMIAL or PDF command to generate the table given in b. Also tabulate the opportunity losses, so you can finally compute the EOL for n=80,and so verify your answer to g. Now it is easy to repeat this. for n=79.then n=78, etc, to verify there is no better n.)