Question:

Problem 6.1 (DoubleTree.)DoubleTree in Austin has 150 standard rooms. DoubleTree generally sells those rooms through two channels, one through their own website, call center and front desk usually at a high rate and the other through agencies, like Priceline at a low rate. Suppose DoubleTree charges a high rate at $150 per room per night through their own channel (they never mark down the price through their own explicit channel to avoid any bad gambling image which hurts reputation) while "implicitly" sells some rooms to the agencies at a low rate of $100 per room per night. Bargain customers who seek low rate usually will buy far in advance of the premium customers through the agency channel. To make it simple, suppose the customers always stay for one night, there is ample demand from the bargain customers for the low rate, and the number of premium customers is however uncertain which is distributed according to the following table:

Number of High-Fare Customers

Probability

80

0.10

90

0.10

100

0.15

110

0.25

120

0.20

130

0.20

(a) How many rooms shall DoubleTree sell to the agencies like Priceline in advance?

(b) What is the total expected revenue (including both low and high rate customers) that DoubleTree can obtain based on your solution to (a)?

(c) The number of no-shows at DoubleTree has a distribution as that in the following table. DoubleTree estimates the cost of bumping a customer is $300. What is the optimal maximum number of reservations to accept per day (suppose overbooked rooms are only sold to the agency channel at $100)?

Number of No-shows

Probability

0

0.05

1

0.05

2

0.05

3

0.10

4

0.25

5

0.20

6

0.20

7

0.10

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Problem 6.2 (NorthEast Airways.) A newly created NorthEast Airways (NE) flight from Philadelphia to Boston has 300 seats. The high fare on the flight is $300 and the restricted/low fare is $150. There is ample demand for the low fare class but high fare demand is random. Further, the customers who buy low fares buy their tickets well in advance before high fare customers. Assume the demand for the high fare is normally distributed with mean 150 and standard deviation of 50.

(a) Mr.Wright is in charge of the flight booking operations and decides to set a protection level for the high fare. What is the optimal protection level for the high fare?

(b) Suppose a protection level of 190 is chosen. What is the expected revenue from high fare passengers?

(c) NE Airways has noticed no shows on the flight. Therefore it has decided to implement a policy of overbooking. The number of no-shows is distributed in a normal distribution with mean of 4 and standard deviation of 1. But overbooking may require bumping passengers off the flight, which has a net cost estimated at $450 per bumped passenger. What is the optimal maximum number of reservations to accept on the flight?