The management of Alaska Airlines has decided to base its overbooking policy of a stochastic single period model to maximize expected profit. This policy now needs to be implemented on a new flight from Seattle to Atlanta. The aircraft has 125 seats available for a one-way fare of $250. However, since there are commonly a few no-shows, the airline accepts more than 125 reservations. On those occasions when more than 125 people arrive to take the flight, the airline finds volunteers to be put on a later flight in return for a certificate worth $150 toward any future travel on Alaska Airlines.
Based on previous experience with similar flights, it is estimated that the relative frequency of no-shows will be as indicated below:
Number of No-Shows Relative Frequency
0 5%
1 10%
2 15%
3 15%
4 15%
5 15%
6 10%
7 10%
8 5%
a. Determine the number of overbooking reservations to accept for this flight.
From the above diagram, we can compute the expected number of overbooking reservations to accept for this flight as follows. Use a formula for the expected value, we have So, the number of overbooking reservations to accept for this flight is 3.9
You could take 4 by rounding it up.