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

Critical value (z) = (overbooked - mean)/ std dev = (4-6)/3 = -0.67

Corresponding service level = NORMSDIST(-0.67) = 0.2525

When the hotel overbooks one room less than the cancellations, it loses equivalent to the average room rate ($ 100). Therefore, underage cost, Cu = 100

Cu/(Cu+Co) = 0.2525 , where Co is the cost of overbooking a room

Co = (Cu/0.2525) - Cu = 296

ANSWER: 296

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