A hotel near the university always fills up on the evening before football games

Question

A hotel near the university always fills up on the evening before football games. History has shown that when the hotel is fully booked, the number of last-minute cancellations has a mean of 6 and a standard deviation of 3. The hotel has overbook 4 rooms. The average room rate is $100. When the hotel is overbooked, policy is to find a room in a near-by hotel and to pay for the room for the customer. This usually costs the hotel certain amount of moneysince rooms booked on such late notice are expensive. What would be the rate that the hotel will have to pay to a near-by hotel (in other words, what is the cost of overbooking a room)?

Explanation / Answer

Hotel are having this problem of last minute cancellations, therefore hotels follows the practice of overbooking.

In the present case number of last-minute cancelaations has a mean of 6 and a standard deviation of 3.

The average room rate is $100, therefore cost of underestimating the cancellation is Cu = 100

Cost of overestimating the cancellations is the cost of room booked such late (more than Cu) is Co

Therefore the critical ratio p needs to be <= 100 / (100+Co)

Hotel has overbooked 4 rooms. Standard Normal Z =( X-mean)/S.D. = -2/3 for which p=.25

therefore 100/(100+Co) = .25 means .25Co = 100 - 25 implies Co = 75/.25 = 300

Cost of overbooking is $300

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