Question:
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.