The Astana airline always books more passengers on a flight than its capacity because of last minutes cancellations. The airline charges $835 per passenger from Almaty (Kazakhstan) to Frankfurt (Germany). However, due to overbooking, it asks a few passengers travelling more than the plane’s capacity to take another flight and offers a coupon of $350, including hotel, meal, etc. The experience has shown the following probability distribution corresponding to no-shows: Number of no-shows Probabillity 0 0.05 1 0.08 2 0.12 3 0.19 4 0.25 5 0.15 6 0.11 7 0.05 The airline hires you as a consultant because you have taken a course in supply chain management. What is the average number of no-shows based on the above distribution? How many overbookings should be made to minimize loss due to no shows, given the above probability distribution? Suppose you find out that last minute no-shows are normally distributed with a mean as determined in (a) above and a standard deviation of 3. How many overbookings would you recommend for minimizing the cost of overestimation and underestimation? Suppose that no-shows have a uniform distribution, that is, equally distributed between 6 and 11. How many overbookings would you recommend for minimizing the cost of overestimation and underestimation?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 30P

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The Astana airline always books more passengers on a flight than its capacity because of last minutes cancellations. The airline charges $835 per passenger from Almaty (Kazakhstan) to Frankfurt (Germany). However, due to overbooking, it asks a few passengers travelling more than the plane’s capacity to take another flight and offers a coupon of $350, including hotel, meal, etc. The experience has shown the following probability distribution corresponding to no-shows:

Number of no-shows	Probabillity
0	0.05
1	0.08
2	0.12
3	0.19
4	0.25
5	0.15
6	0.11
7	0.05

The airline hires you as a consultant because you have taken a course in supply chain management. What is the average number of no-shows based on the above distribution?
How many overbookings should be made to minimize loss due to no shows, given the above probability distribution?
Suppose you find out that last minute no-shows are normally distributed with a mean as determined in (a) above and a standard deviation of 3. How many overbookings would you recommend for minimizing the cost of overestimation and underestimation?
Suppose that no-shows have a uniform distribution, that is, equally distributed between 6 and 11. How many overbookings would you recommend for minimizing the cost of overestimation and underestimation?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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