Managing Fixed Capacity - Operations Management

Please show all answers using the 2 decimal places convention (do NOT round an intermediate or final answer to a whole number). Remember to show all work leading to the final answer.

Question 1

The Curtis M Philips Center for the Performing Arts at UF is staging Hamilton on a specific night in May 2023. With a fixed capacity of 1700 seats in the proscenium hall, the focus is on maximizing occupancy for the show.

Based on historical data, it is estimated that if the seats are offered at a low price of $ pL=25 per seat, all 1700 seats will be sold. The Center is also contemplating offering one of three high prices for the same seats - $ p2=50 per seat; $ p2=75 per seat; or $ p2=100 per seat. Demand at each of these high prices (i.e., p2) is normally distributed such that: if the high rate of $ 50 is offered, then =1000 and =300; if the high rate of $ 75 is offered, then =900 and =300; and if the high rate of $ 100 is offered, then =800 and =300.

To start with, showing all supporting analytics, complete the following table.

High Price	Protection level (seats)	Booking limit (seats)	Demand Lost (seats)	Expected Sales at high-rate (seats)	Capacity Utilization (%)	Expected Total Profit ($)
$ 50
$ 75
$ 100

Based on the results in the table, answer the following questions:

Which high price should be chosen if the manager wants to offer the maximum number of seats to those willing to pay the low price of $ 25.

Which high price should be chosen if the manager wants to minimize the demand lost (in seats)?

Which high price should be chosen if the manager wants to maximize capacity utilization?

Which high price should be chosen if the manager wants to maximize expected total profit?

Question 2

On a given GNV-ATL flight, there are 200 seats and each seat is sold at an average ticket price of $ 300. It has been observed that on most days in the past month, the flight rarely approaches 100% occupancy since there are passenger no-shows. Hence, the airline

decides to overbook flights. The airline manager assigned the task of determining the number of seats to overbook on this flight starts by estimating no-shows using historical information. However, she encounters an interesting conundrum: both the mean and std. deviation of no-shows changes based on the rate offered to customers with a confirmed booking who are denied service referred to as the service denial rate.

Three specific service denial rates being contemplated by the airline manager and their associated mean and standard deviation of no-shows are: (a) service denial rate = $ 400, mean = 28, std deviation = 12; (b) service denial rate = $ 500, mean = 24, std deviation = 12; and (c) service denial rate = $ 600, mean = 20, std deviation = 12. It is safe to assume that the distribution of no-shows for each service denial rate is normal.

To start with, showing all supporting analytics, complete the following table.

Service Denial Rate	Optimal Overbooks Y* (seats)	Percentage of time passengers with a confirmed reservation will be denied a seat (%)	Expected number of passengers with a confirmed reservation who will be denied a seat	Expected Loss from denying a seat to passengers with a confirmed reservation ($)	Expected number of empty seats	Expected loss from empty seats ($)
$ 400
$ 500
$ 600

Based on the results in the table, answer the following questions:

Which service denial rate should be chosen if the manager wants to minimize the percentage of time customers with a confirmed reservation will be denied a seat?

Which service denial rate should be chosen if the manager wants to minimize the Expected number of passengers with a confirmed reservation who will be denied a seat?

Which service denial rate should be chosen if the manager wants to minimize the expected Loss from denying a seat to passengers with a confirmed reservation

Which service denial rate should be chosen if the manager wants to minimize the Expected loss from empty seats?