Question

Seats for Sale

State's football program has risen to the ranks of the elite with postseason bowl games in each of the past 10 years, including a national championship game. The Bruins (as the fans are called) fill the stadium each game. Season tickets are increasingly difficult to find. In response to the outstanding fan support, State has decided to use its bowl revenues to expand the stadium to 75,000 seats.
The administration is confident that all 75,000 seats can be sold at the normal price of $40 per game ticket; however, Frank Pinto's job, as athletic director, is to get as much revenue out of the stadium expansion as possible. In addition to stadium boxes for wealthy alums, Frank would like to take this opportunity to repurpose existing seats. A certain number of seats (yet to be determined) would be set aside for premium ticket holders who would pay $200 per ticket for the privilege of 50-yard line seats with chair backs and access to indoor concessions. The question is, how many fans would be willing to pay such a premium? If too many seats are designated in the premium sections, they could remain vacant. Too few premium seats would lose potential revenue for the program.
Frank has decided that if the plan has any chance of success, unsold premium seats should not be sold at reduced rates. It would be better to donate them to local charities instead. Gathering data from his cohorts at peer institutions, Frank has put together the following probability distribution of premium ticket holders. The data begin with 1000 tickets since Frank already has requests for 999 tickets from alumni donors. He is asking for your help in performing the analysis.
No. of Premium Tickets Probability
1,000 0.10
5,000 0.30
10,000 0.24
15,000 0.15
20,000 0.10
25,000 0.06
30,000 0.05
a. Using revenue management, determine how many seats should be reserved for premium ticket holders.
b. Considering your answer to part (a) and the possible outcomes listed above, how much total revenue (i.e., regular and premium) can be expected from ticket sales?
c. The administration is unsure about Frank's plan. The VP of finance thinks an expected value of the number of premium seats would produce better results. How would the number of premium seats change using expected value? Considering the possible outcomes, which approach yields the most potential revenue?

Answer 1

a. To determine how many seats should be reserved for premium ticket holders, Frank can use revenue management techniques. One common method is to use the expected revenue per seat, which is calculated by multiplying the number of seats by the expected price per seat and then multiplying that by the probability of that number of seats being sold. Frank can then compare the expected revenues for different numbers of premium seats and choose the number of seats that maximizes the expected revenue.

b. If the number of premium seats is 1,000, then the expected revenue is:

(1,000 x $200 x 0.10) + (75,000 - 1,000) x $40 x 1 = $200,000 + $3,000,000 = $3,200,000

If the number of premium seats is 5,000, then the expected revenue is:

(5,000 x $200 x 0.30) + (75,000 - 5,000) x $40 x 0.7 = $3,000,000 + $2,330,000 = $5,330,000

If the number of premium seats is 10,000, then the expected revenue is:

(10,000 x $200 x 0.24) + (75,000 - 10,000) x $40 x 0.76 = $4,800,000 + $3,768,000 = $8,568,000

and so on for the rest of the numbers.

From the above calculations, we see that the expected revenue is maximized at 10,000 premium seats, which is expected to generate $8,568,000.

c. Using the expected value of the number of premium seats would be calculated by multiplying the number of seats by its probability. The expected value of the number of premium seats is:

1,000 x 0.10 + 5,000 x 0.30 + 10,000 x 0.24 + 15,000 x 0.15 + 20,000 x 0.10 + 25,000 x 0.06 + 30,000 x 0.05 = 10,000.

Comparing this with the number of seats obtained by maximizing the expected revenue (10,000), we see that both approaches yield the same number of premium seats. This means that both approaches would yield the same potential revenue.