An airline flies daily from San Francisco to Chicago. Most of the passengers are

Question

An airline flies daily from San Francisco to Chicago. Most of the passengers are business travelers. There are 150 seats available in the single cabin plane. The average ticket price is $300 per seat. All fares are non-refundable, so no-shows forfeit the entire fare The fixed cost to operate the flight is $30,000. The airline s revenue management analysts estimate that the demand for this flight is normal y distributed with a mean of 195 reservation requests and a standard deviation of30. The anal lysts also believe th only 80% of the travelers wi ho make a reservation will shot w up for the flight. That is, on any flight there is on average 20% who do not show and forfeit their fare. The airline's revenue management analysts have decided to investigate the effect of raising the number of reservations to accept for this flight to 190 (in the past only 165 reservations were accepted, but this led to a lot of empty seats because ofno shows) When a customer is bumped from a flight, the airline places the bumped passenger on the next flight and compensates the bumped passenger for the inconvenience. The airline estimates that the total cost of bumping a passenger is $450 The airline's revenue management analysts want to investigate the effect that accepting 190 reservations w ill have on the following performan ce measures: the overall profit of each flight, the average number of filled seats the probability that the flight will be full and the average number of bumped passengers. To conduct it analysis, the revenue management analysts will develop a spreadsheet simulation model. The spreadsheet simulation will model the demand for tickets as a normally distributed random variable with a mean of 195 and a tandard deviation of 30. The number of ticketed passengers that show up for the flight is modeled as a binomial random variable with a probability of showing up that is 0.80 (this means the probability ofno-shows is 1 0.80 0.20). The binomial distribution is appropriate because the random event of interest is number of passengers with tickets w ho show up for the flight Complete the simulation spreadsheet provide d. Recall that a normally distributed random variable can be generated using the NORM.INV function in Excel. The number of passengers who show up for the flight can be simulated using the BINOM.INV function in Excel. That function looks like binominy, trials, probability of success, alpha). In this instance the trials are equal to the tickets sold. The probability of showing up is 0.80 and the alpha value is computed random using Excel's rand 0 function. Replicate the simulation 500 times keeping track of number offilled seats, number denied boarding (bumped) and profit. From the 500 replications compute the average number of bumped passengers, the average profit, and the relative frequency that the flight is full (i.e., has 150 or more filled seats

Explanation / Answer

showing only 100 simulations as there is 65000 chars limits. Formulae are shown at the beginning

avg no. of bumped 2.05 or 3 approx avg bumped costs                             921 avg profit                       23,315 frequency when flight is full                             303 % when flight is full 61%

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