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 25 customers (with a standard deviation of 13) cancel their reservation or do not show for the flight. Revenue from a ticket on the flight is $135. 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 $218. 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

Let Super discount overbook x seats

Let probability of cancellation=p

Thus probability that seat will not be cancelled =1-p

If seat is cancelled the refund amount=135*x*p

If seat is not cancelled the cost incurred=218*x*(1-p)

For breakeven both loss should be equal

135xp=218x(1-p)

135xp=218x-218xp

353xp=218x

p=218/353=0.617564

For p=0.6175, z=0.3

Thus The overbooking seat =Mean + z*S.D=25+0.3*13=28.9

Or The Super discount should overbook 29 seats

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