Kennedy Murphy, Zhongxu Zhao, Alexis ChristieCost of
Compensation for Overbooked PassengersGoalsDesign an overbooking
policy for an airportRun simulationsAnalyze the potential cost of
compensationOptimal OverbookingDuke Mathematics Department
Randomly Generate Number of PassengersBinomial
distributionProbability mass function:P(X=k) = n! pk (1-p)n-k
k!(n-k)!
p = probability of one passenger showing up for their flight =
0.851-p = probability of failure = 0.15n = overbooking maximumk =
number of passengers who show up
Randomly Generate Number of PassengersEx. For a plane with a
maximum capacity of 150 passengers and an overbooking maximum of
177 passengers, the probability that 156 passengers will show up
is:
Monte Carlo SimulationUsed to simulate values of a discrete
random variableWant to generate a random number of passengers based
on binomial distribution
