Question 1: The Hyatt hotel in Kansas City has 150 rooms with standard king beds and two rates: a full price of $200 per night and a discount price of $120 per night. To receive the discount price, a customer must purchase the room at least two weeks in advance. For a particular night, the hotel estimates that the demand from leisure travelers (who book at the discounted price) could fill the whole hotel while the demand from the business travelers (who book at the full price) is distributed normally with a mean of 70 rooms and a SD of 29 rooms.
a. Find the optimal protection level (i.e., the number of rooms to be protected for business travelers) for full-price rooms.
b. The Sheraton hotel nearby declared a fare war by slashing business travelers' price down to $150.
The Hyatt had to match that price to keep the demand at the same level. How does the optimal protection level change?
c. What numbers of rooms on average remain unfilled if Hyatt establishes a protection level of 61 rooms?
d. If Hyatt were able to ensure that every full-price customer would receive a room, what would its expected revenue be?
e. If Hyatt did not protect any rooms for the full-price customers and if leisure travelers booked before the business travelers, then what would the expected revenue be?
f. Taking the assumptions in part (e) above, and assuming that Hyatt protects 50 rooms for the full price, what is its expected revenue?
Question 2:
You are in charge of designing a supply chain for furniture distribution. One of your products is a study desk. This desk comes in two colors: oak and cherry. Weekly demand for each desk type is normal with a mean of 100 and a standard deviation of 65. The demands for the two colors are independent. A customer looking for a cherry desk will not buy the oak desk if the cherry one is out of stock and vice versa. The lead time from the assembly plant to retail store is two weeks and you order inventory replenishments weekly. There is no finished goods inventory at the factory (desks are assembled to order at the factory).
a) What is the expected on-hand inventory of desks at the store (oak and cherry together) at the start of a week if you maintain a 97% in-stock probability for each desk color?
b) What is the expected on-hand inventory of desks at the store (oak and cherry together) at the start of a week if you maintain a 97% fill rate for each desk color?
You, as manager, notice that only the top part of the desk is oak or cherry; the remainder (base) is made of standard grey metal. Hence you suggest that the store stock oak and cherry tops separately from grey bases and assemble them at the store when demand occurs. Assume, once again, that the demands for the two colors are independent, and that a customer looking for a cherry desk will not buy the oak desk if the cherry is out of stock and vice versa. The replenishment lead time is still two weeks, and you still order weekly. The same 97% fill rate is maintained.
c) What is the expected on-hand inventory of oak and cherry tops at the start of a week now?
d) How much less inventory of grey bases do you have on average at the store at the start of a week with the new in-store assembly scheme relative to the original system in which desks are delivered fully assembled?