IEOR 3402: Assignment 10

• Do not hand it in.

1. The Inn at Columbia has 150 rooms with standard queen-size beds and two two rates: a full price of $200 and a discount price of $120. To receive the discount price, a customer must purchase the room at least two weeks in advance (this helps to distinguish between leisure travelers, who tend to book early, and business travelers, who value the flexibility of booking late). For a particular Tuesday night, the hotel estimates that the demand from leisure travelers could fill the whole hotel while the demand demand from business travelers is distributed normally with a mean of 70 rooms and a standard deviation of 29.

(a) Suppose 50 rooms protected for full-price rooms. What is the booking limit for the discount rooms?
(b) Find the optimal protection level for full-price rooms (the number of rooms to be protected from sale at a discounted price).
(c) The Sheraton declared a fare war by slashing business travelers' prices down to $150. The Inn at Columbia had to match that fare to keep demand at the same level. Does the optimal protection level increase, decrease, or remain the same? Explain your answer.
(d) What number of rooms (on average) remain unfilled if we establish a protection level of 61 for the full-priced rooms?
(e) If The Inn were able sell no room to the leisure travelers, what would the Inn's expected revenue be?
(f) If The Inn did not choose to protect any rooms for the full price and leisure travelers book before business travelers, then what would the Inn's expected revenue be?
(g) If The Inn protects 50 rooms for the full price, what would the Inn's expected revenue be?

2. Due to customer no-shows, the Inn at Columbia is considering implementing overbooking. Recall that the Inn at Columbia has 150 rooms, the full fare is $200, and the discount fare is $120. The forecast of no-show is Poisson with a mean of 15.5. The Inn is sensitive about the quality of service it provides alumni, so it estimates the cost of failing to hone a reservation is $325 in lost goodwill and explicit expenses.
(a) Should the optimal overbooking limit (the maximum reservations above the available 150 rooms that the Inn should accept) be more or less than 10 rooms?
(b) If the Inn accepts 160 reservations, what is the probability that the Inn will not be able to honor at least one reservation?
(c) If the Inn accepts 165 reservations, what is the probability that The Inn will be fully occupied?
(d) If the Inn accepts 170 reservations, what is the expected total cost incurred due to bumped customers?