Question

Next week, Super Discount Airlines has a fight from New York to Los Angeles that will be booked to capacity. The airline knows from past history that an average of 25 customers (with a standard deviation of 15) cancel their reservation or do not show for the fight. Revenue from a ticket on the fight is $125. If the fight is overbooked, the airline has a policy of getting the customer on the next available flight and giving the person a free round-trip ticket on a future fight. The cost of this free round-trip ticket averages $250. Super Discount considers the cost of flying the plane from New York to Los Angeles a sunk cost. By how many seats should Super Discount overbook the fight?

Answer 1

Answer:

The cost of underestimating demand is considered a revenue loss that arises due to cancellation of flight costing $125. Hence, cost of underestimating the demand is, $C_{u}$ = $125 .

The cost of overestimating the demand is known as rewards. For example. free round trip ticket worth $250. Hence. cost of overestimating the demand. $C_{o}$ = $250 .

Denote the optimal probability of tickets not being sold by P. The expression is shown below:

$P = \frac{C_{u} }{C_{o} + C_{u} }$

$P = \frac{125}{250 + 125}$

P = 0.3333

Hence. the optimal probability that the tickets are not being sold is 0.33.

Apply the formula, NORMSINV (0.3333) in the Excel spreadsheet

The value of z is obtained as -0.4308. The negative value of z indicates that the number of seats to be overbooked must be less than an average of 25.

As per the stated question, an average of 25 customers cancel or do not show for the flight. Also the standard deviation is 15.

Calculate the number of seats by which company SD should overbook the flight.

= Value of z x Standard deviation

= -0.4308 x (15)

= -6.462

Subtract the value. 6 from the average customers that do not show up for the flight.

25 - 6 = 19 seats

Hence, the airlines should overbook the flight by 19 seats .