Cost of Compensation for Overbooked Passengers

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

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! pk(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 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*00< 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