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 5 and standard deviation of 3. The average room rate is $80. When the hotel is overbooked, policy is to find a room in a nearby hotel and to pay for the room for the customer. This usually costs the hotel approximately $200 since rooms booked on such late notice are expensive. How many rooms should the hotel overbook?

Answer 1

Cost of underbooking, Cu = $80

Cost of overbooking, Co = $200

Critical ratio = Cu / ( Cu+Co) = 80/280 = 0.2857

For service level of 0.2857, z score = -0.56

Optimal overbooking = mean + Z* standard deviation = 5+ -0.56 *3 = 3.30 rooms