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Airline Overbooking:

Another Example Simulation Problem

You are taking reservations for an airline flight. This particular
flight uses an aircraft with 50 first-class seats and 190
economy-class seats.

First-class tickets on the flight cost $600, with demand to purchase
them distributed like a Poisson random variable with mean 50. Each
passenger who buys a first-class ticket has a 93% chance of showing up
for the flight. If a first-class passenger does not show up, he or
she can return their unused ticket for a full refund. Any first class
passengers who show up for the flight with tickets but are denied
boarding are entitled to a full refund plus a $500 inconvenience
penalty.

Economy tickets cost $300. Demand for them is Poisson distributed
with a mean of 200, and is independent of the demand for first-class
tickets. Each ticket holder has a 96% chance of showing up for the
flight, and "no shows" are not entitled to any refund. If an economy
ticket holder shows up and is denied a seat, however, they get a full
refund plus a $200 penalty. If there are free seats in first class
and economy is full, economy ticket holders can be seated in first
class.

The airline allows itself to sell somewhat more tickets than
it has seats. This is a common practice called "overbooking". The firm is
considering the 18 possible polices obtained through all possible combinations
of

- Allowing overbooking of up to 0, 5, or 10 first-class seats

- Allowing overbooking of up to 0, 5, 10, 15, 20, or 25 economy seats

Which option gives the highest average profit? What are the average
numbers of first-class and economy passengers denied seating under this
policy. If no overbooking of first class is allowed, what is the best
policy?