Hotel manager Basil Fawlty and his resourceful assistant Manuel run a 26 room ho

Question

Hotel manager Basil Fawlty and his resourceful assistant Manuel run a 26 room hotel in a
quaint little town called Tourkey on the eastern sea coast. A combination of Mr. Fawlty’s
genial attitude and the absence of a respectable inn in the nearby vicinity imply that Mr.
Fawlty enjoys ample demand at his low fare of $159 per night.
Manuel notes that some customers will walk into the inn requesting a room for that evening
and they are willing to pay a high fare of $325 per night. Manuel knows this demand is
variable. (In reality, this demand is Poisson distributed with mean 7.5). He suggests some
rooms should be kept unsold to the low fare customers, so that they can serve the high fare
customers.
1. To maximize profits with Manuel’s plan, what is the booking limit that should be set
for low fare customers?
2. On average, how many empty rooms will the hotel have under Manuel’s plan, if the
protection level is 9 rooms?
3. Basil scoffs at the idea: “Empty rooms! A bird in hand is better than two in the bush.
This brilliant idea of yours, Manuel, might work in Barcelona but definitely not at
Tourkey. Let me run the hotel my way. We will sell to everyone who reserves in
advance and ignore the walk?in demand”. If Basil has his way, what will be the
hotel’s expected revenue?
4. Manuel replies: “If you are going to forgo the opportunity to sell to last minute
customers, let’s at least accept more than 26 reservations for the evening.” Checking
the data, Manuel observes that the number of “no-shows” is Poisson distributed with
mean 2.75. (Recall, a “no-show” is when a customer makes a reservation but doesn’t
show up to use the room that evening.) Manuel also notes that a $100 non-refundable
deposit is required with all reservations. However, if the hotel does not have a room
for a reservation holder, then they need to book that person in a B&B in the nearest
town. They decide that in those cases they would refund the customer’s deposit, and
pay for the customer’s stay in the B&B, which is $450. The customer would not be
happy, but they are getting a free night, so Manuel figures that there would be no loss
of good will. Finally, if they have an empty room due to a no-show, they also figure
that they would not be able to fill the room with a last minute customer. What is the
critical ratio they should use to choose an overbooking quantity to maximize revenue?

Explanation / Answer

A)

Co = 159, Cu = 325-159. Critical ratio is 0.5108. Based on the critical ratio,the Protection Level for the Poisson distribution with mean 7.5 is 7. therefore, the booking Limit is 26-7 = 19 rooms

B)

  Recall that left over inventory = empty rooms. For Poisson demand distributionwith mean 7.5, the expected empty rooms with protection level of 9 is L(9) = 0.52292 andLeft over inventory = 9 - 7.5 + 0.52292 = 2.023

C)

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