Question

On a given San Jose –New York City United Airlines flight, there are200 seats.The high fare is $675 and the low fare is $375. Demand for the low fare is abundant while demand for the high fare is normally distributed with a mean of 80 and standard deviation 35. Suppose there is no overbooking. a)Suppose 60 seats are protected for the high fare seats.What is the booking limit for the low fare seat? b)Find the optimal protection level for high fare seats (the number of seats to be protected from sale at the low fare).c)Southwestern Airlines declared a fare war by slashing high fare down to $500. United Airlines had to match that fare to keep demand at the same level. Does the optimal protection level increase, decrease, or remain the same? Explain your answer. d)If United Airlines did not choose to protect any seats for the high fare,and low fare book before high fare, then what would United Airlines’ expected revenue be?e)If United Airlines were able to ensure that every high fare would receive a seat, what would United Airlines’ expected revenue be? f)Based on past experience, the number of passengers who reserve a seat but do not show up for departure is normally distributed with mean 20 and standard deviation 10. United Airlines decided to overbook the flight and estimated that the average loss from a passenger who will have to be bumped (if the number of passengers exceeds the number of seats) is $800. What is the maximum number of reservations that should be accepted? g)If overbooking is allowed as in part (f), then what is the booking limit for the low fare seat?

Answer 1

Full fare, pf = $ 675

Low fare, pd = $ 375

mean demand for high fare, m = 80

standard deviation fo demand for high fare, s = 35

a) Total number of seats = 200

High fare seats protected = 60

Booking limit for low fare seats = 200 - 60 = 140

b) Critical fractile for protection of high fare seats = (pf - pd)/pf

= (675 - 375)/675

= 0.444

z value = NORMSINV(.444) = -0.14

Optimal protection level for high fare seats = m + z * s

= 80 + (-0.14)*35

= 75

c) Protection level for high fare seats will decrease, because the incremental profit of high fare seats over low fare seats is lesser than before. Therefore, lesser number of seats must be protected for high fare.

Critical fractile = (500-375)/500 = 0.25, z = NORMSINV(0.25) = -0.6745

New Protection level for high fare seats = 80 + (-0.6745)*35 = 56

d) It is given that demand for low fare is abundant, So, if low fare is booked before high fare, then all the seats will be booked in low fare.

Expected revenue = 200*375 = $ 75,000