Problem
At this stage of the contract, AA's operations manager must specify the seating configuration on the airplane that will be used on the Charlotte - Miami - New York City - Charlotte circuit. AA flies this circuit once per day.
The configuration decision involves specifying how many rows will be allocated for business-class seats and how many for coach seats. Each business-class row contains 4 seats and each coach row contains 6 seats. If the aircraft were configured entirely of coach rows, there would be 40 rows. Business-class seats are wider and afford more legroom, so that, in order to make room for one business-class row, two coach rows must be removed. Thus, conversion from coach to business-class seating involves the loss of some seats, but this loss might be compensated from the higher prices paid by the business-class passengers. The revenues rates for business-class and coach seats are given below.
Table 1: Revenue per Seat
|
|
Business-class
|
Coach
|
|
Charlotte - Miami
|
$550
|
$300
|
|
Miami - New York City
|
$400
|
175
|
|
New York City - Charlotte
|
$450
|
$200
|
A perfect match between the configuration and the demand for seats is seldom possible. Historical data suggests a probability of demand for seats on each leg (as detailed below).
Table 2: Distribution of Total Demand for Seats
|
|
Minimum
|
Most Likely
|
Maximum
|
|
Charlotte - Miami
|
160
|
180
|
220
|
|
Miami - New York City
|
140
|
200
|
240
|
|
New York City - Charlotte
|
150
|
200
|
225
|
There is another distribution for the fraction of demand that corresponds to business-class seats (given below). While demand seems to vary on each leg of the circuit, this distribution of fraction applies on all legs. It is assumed that if a passenger cannot book a seat in the seating category he/she intends to book, then he/she will simply buy a seat from AA's competitors.
Table 3: Distribution of Fraction Business Class
|
Fraction of Business-Class
|
Probability
|
|
5%
|
0.2
|
|
12%
|
0.5
|
|
15%
|
0.3
|
The fixed cost of operating the airplane is $125,000 per day for the full circuit. AA is seeking a profit-maximizing configuration.
Task
• Suppose that AA is considering a plane configuration that has 3 rows of business-class seats and 34 rows of coach seats. Create a spreadsheet model for this problem and replicate it 1000 times.
o What is the minimum, average, maximum profit per day for this configuration?
o What is the probability that AA will earn a positive profit on this circuit? Establish a 95% confidence interval for the probability of AA earning a positive profit on this circuit.
o What is the optimal seat configuration that maximizes AA's expected profit from the circuit? Use psi sim param function to find the answer.