Question

Q3. 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? (5 points) Number of no- shows 0 Probability 0.01 0.10 0.63 0.26 2 en

please show your work

Answer 1

First let us assume that the cost of the ticket is $ 100.

Now as it is given in the question the compensation cost or the cost of bumping the passenger is 10 times than the ticket price = 10*100 = 1000 $

Now let us calculate the cost of the airlines for each overbooking scenario :

Scenario 1 : Overbooked Seat = 0

No Shows	Probablity	Cost in $
0	0.01	0
1	0.1	100
2	0.63	200
3	0.26	300
Total Cost	=	(0*0.01) + (100*0.1) + (200*0.63) + ( 300*0.26) = 10 + 126 + 78 = 214

Scenario 2 : Overbooked Seat = 1

No Shows	Probablity	Cost in $
0	0.01	10*100 = 1000
1	0.1	0
2	0.63	100
3	0.26	200
Total Cost	=	(1000*0.01) + (0*0.1) + (100*0.63) + ( 200*0.26) = 52 + 63 + 10 = 125

Scenario 3 : Overbooked Seat = 2

No Shows	Probablity	Cost in $
0	0.01	2*10*100 = 2000
1	0.1	1000
2	0.63	0
3	0.26	100
Total Cost	=	(2000*0.01) + (1000*0.1) + (0*0.63) + ( 100*0.26) = 20 + 100 +26 = 146

Scenario 4 : Overbooked Seat = 3

No Shows	Probablity	Cost in $
0	0.01	3*10*100 = 3000
1	0.1	2000
2	0.63	1000
3	0.26	0
Total Cost	=	(3000*0.01) + (2000*0.1) + (1000*0.63) + ( 0*0.26) = 30 + 200 + 630 = 860

As we can see from the above scenarios :

The Seats Overbooked and the Total Cost incurred for the airline are :

Seats Overbooked	Total Cost Incurred $
0	214
1	125
2	146
3	860

As we can see the total cost is the minimum at over-booked seats = 1 and then keeps on increasing , so in order to minimise the total cost the best case scenario for the airlines is to overbook = 1 seat.