1. Kennedy Murphy, Zhongxu Zhao, Alexis Christie Cost of Compensation for Overbooked Passengers

2. Goals Design an overbooking policy for an airport Run simulations Analyze the potential cost of compensation

3. “Optimal Overbooking” Duke Mathematics Department

4. Randomly Generate Number of Passengers Binomial distribution Probability mass function: P(X=k) = n! p k (1-p) n-k k!(n-k)! p = probability of one passenger showing up for their flight = 0.85 1-p = probability of failure = 0.15 n = overbooking maximum k = number of passengers who show up

5. Randomly Generate Number of Passengers Ex. 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: P(X=156) = 177 (0.85) 156 (1-0.85) 177-156 156 = 0.071

6. Monte Carlo Simulation Used to simulate values of a discrete random variable Want to generate a random number of passengers based on binomial distribution RangeProbability (Pb) 1<=X<=1500.29 151<=X<=1600.65 161<=X<=1700.05 171<=X<=1800.00 PbPm 0P<0.29 0.290.29<=P<0.94 0.940.94<=P<0.99 0.99 0.99<=P http://office.microsoft.com/en-ca/excel-help/introduction-to-monte-carlo-simulation-HA001111893.aspx

7. Assumptions Maximum wait time = 24 hr (1440 min) Everyone that gets kicked off the plane waits the same amount of time for their next flight (i.e. all passengers kicked off the plane are rebooked on the same flight) # of volunteers = 5 (approx. 3% of flight population) We always rebook passengers on our own company’s flights Ticket price = $230 (one way) Based on Air Canada rate for flight from Halifax to Toronto on a Wednesday at the end of November (i.e. typical day to fly)

8. Volunteers U(v) = cost of volunteers v = # of volunteers We pay each volunteer $200 cash. Thus, U(v) = 200v

9. Passengers Forced Off Plane M(t, f,m) = cost of passengers involuntarily forced off plane t = wait time f = fair price (i.e. ticket price) m = # of people forced off plane M(t, f,m) = m*0 0< t <=1 m*min(2f, f + 200) 1< t <=2 m*min(3f, f + 400) 2<=t M(t, 230,m) = m*0 0< t <=1 m*min(460, 430) 1< t <=2 m*min(690, 630) 2<=t

10. Total Cost C(v,m,t,f) = U + M = cost of compensating both volunteers and passengers forced off plane

11. Simulation

12. Future Work “goodwill” cost Distribution for volunteers Altering the wait time distribution Rebook on outside airlines Individualized wait times