A small airline is trying to determine how many seats to overbook. The airline e

Question

A small airline is trying to determine how many seats to overbook. The airline estimates that the cost they experience from a customer that is overbooked is $400. The airline also estimates that lost revenue due to an unsold seat is $275. The airline is willing to consider overbooking up to five seats. The CUMULATIVE probabilities of the number of customer cancellations is shown in the table below. What is the optimal number of seats to overbook?

Seats -------Cumulative Probability

0 --------------0.3

1 --------------0.5

2 --------------0.7

3 --------------0.8

4 --------------0.95

5 --------------1

Explanation / Answer

Cost of Overbooking (Co) - $400 Cost of Underestimating (Cu) - $275 Probability is calculated as P Cu / (Cu + Co) P 275 / (275 + 400) P 275 / 675 P 0.4074 As per table provided below, optimal overbooking comes to 1 seat. Seats -------Cumulative Probability 0 --------------0.3 1 --------------0.5 2 --------------0.7 3 --------------0.8 4 --------------0.95 5 --------------1

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