Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacit

Question

Offwefly Airlines has a daily flight from Sacramento to Las Vegas with a capacity of 100 passengers. On average, 17 ticket holders cancel their reservations at the last minute, so the company intentionally overbooks the flight. Cancellations can be described by a normal distribution with a standard deviation of 4.6. Profit per passenger is $190. If a passenger arrives but cannot board due to overbooking, the company policy is to provide compensation of $150.

What is the optimal probability of having too many passengers to seat on the plane?

Explanation / Answer

Mean = 17

Standard deviation = 4.6

Cost of Underbooking Cu = 190

Cost of Over booking Co = 150

Optimum service level = Cu / (Cu + Co)

Optimum service level = 190/(150+190) = 0.5588

From the table provided we get Z value as 0.15

optimal booking = mean+z*standard deviation= 17+(0.15*4.6)

optimal booking = 17.69 or 18

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