Next week, Super Discount Airlines has a flight from New York to Los Angeles tha

Question

Next week, Super Discount Airlines has a flight from New York to Los Angeles that will be booked to capacity. The airline knows from past history that an average of 38 customers (with a standard deviation of 25) cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $137. If the flight 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 flight. The cost of this free round-trip ticket averages $265. 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 flight? (Round your answer to the nearest whole number.)

Explanation / Answer

Cost per unit of demand underestimated, Cu = $ 137

Cost per unit of demand over estimated Co = $ 265

The optimal probability of not being sold, P <= Cu /( Co + Cu) = 137/(137+265) = 0.3408

NORMINV(0.3408), Z score = -0.410291618 , SD = 25,

The average demand forecast is 38 .

Order quantity = Average Demand + (z*SD)

Order Quantity = 38+ (-0.4103*25) = 27.74, Rounding off -> 28 customers.

The Super discount should overbook the flight by 28 passengers.

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