# revenue management

1. Granite State Airlines serves the route between New York and Portsmouth, NH, with a single-flightdaily
100-seat aircraft. The one-way fare for discount tickets is \$100, and the one-way fare for full-fare
tickets is \$150. Discount tickets can be booked up until one week in advance, and all discount
passengers book before all full-fare passengers. Over a long history of observation, the airline
estimates that full-fare demand is normally distributed, with a mean of 56 passengers and a standard
deviation of 23, while discount-fare demand is normally distributed, with a mean of 88 passengers and
a standard deviation of 44.
a) A consultant tells the airline they can maximize expected revenue by optimizing the booking limit.
What is the optimal booking limit? (Hint: Use the standard normal cumulative distribution table)
(10 pts)
b) The airline has been setting a booking limit of 44 on discount demand, to preserve 56 seats for
full-fare demand. What is their expected revenue per flight under this policy? (Hint: First find the
expected revenue when b= 0. Here you can assume Probability{df = k} = Ff(k+0.5) – Ff(k-0.5) and
use a spreadsheet. Then using the recursive formula, find the expected revenue if b is increased
by 1 until it reaches b=44 using a spreadsheet) (20 pts)
c) What is the expected gain from the optimal booking limit over the original booking limit? (20 pts)
d) A low-fare competitor enters the market and Granite State Airlines sees its discount demand drop
to 44 passengers per flight, with a standard-deviation of 30. Full-fare demand is unchanged. What
is the new optimal booking limit? (10 pts)
2. Granite State Airlines also serves the route between Washington, DC (National), and Portsmouth, NH,
with a single flight daily. The airline sells both discount-fare and full-fare tickets. The airline has
assigned a 100-seat aircraft to the flight. Using Littlewood’s rule, the airline has determined that the
optimal discount-fare booking limit for a flight departing in two weeks is 40.
a) What is the protection level for the flight? (10 pts)
b) The flight controller has learned that the annual Yorkshire Terrier Fancier’s Convention will be held
in Portsmouth in two weeks. As a result, he increased the forecast of mean discount-fare demand
by 50% over its previous value. The full fare forecast remained the same. What are the new
booking limits and protection levels for this flight? (10 pts)
c) The full fare for this flight is \$200 and the discount fare is \$100. What is the expected full-fare
demand for this flight, assuming that both discount-fare and full-fare demand follow normal
distributions? (10 pts)
d) Right after learning about the Yorkshire Terrier Fancier’s Convention, the flight controller learned
that, due to maintenance problems, there will also be a switch of aircraft on the flight. Instead of
a 100-seat aircraft, the flight will be served by a 120-seat aircraft. What are the new booking limits
and protection levels for this flight?

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