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# Operations Research : Stochastic single period model to maximize expected profit.

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 Relative Frequency
No-Shows
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.

#### Solution Summary

A stochastic single period model to maximize expected profit is investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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