Question

Green Airways flies several daily flights from Dallas to Chicago with 150-seat planes. Based on historical data, the flight on Wednesday evening before Thanksgiving is always sold-out. However, there are usually no-shows, so the airline decides to improve revenue by overbooking. The distribution of no-shows is according to the table below and the airline estimates that the cost of bumping a passenger is about 10 times more than the ticket price. How many seats should Green Airways overbook? Please show work. Thank you.

Number of no-shows	Probability
0	0.01
1	0.10
2	0.63
3	0.26

Answer 1

Let the ticket price = P

So, the cost of bumping = 10*P

Cost of overbooking one less seat than the number of no-shows, C_u = P
Cost of overbooking one more seat than the number of no-shows, C_o = 10P

So, the optimal in-stock probability = C_u / (C_o + C_u) = P / (10P + P) = 0.09

Number of no-shows	Probability	Cumulative probability
0	0.01	0.01 < 0.09
1	0.10	0.11 > 0.09
2	0.63	0.74
3	0.26	1.00

The cumulative probability crosses the optimal in-stock probability for the number of no-shows=1

So, the optimal overlooking = 1