Operations Research : Stochastic single period model to maximize expected profit.
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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.
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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.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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