A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season.

A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season.

March 18, 2022

A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season. Based on the past experience, the number of no-shows is an approximated normal distribution with a mean of 3 and a standard deviation of 4. The average room rate of the inn is $73/night. The inn's average cost of operating a room is $33/night, no matter it is empty or occupied. Accommodating an overbooked guest is expensive. The inn must book a room with one of the two nearby resorts for the overbooked guest, and pay the difference. Rooms in resort A have an average price of $117/night. The room availability in resort A is 35%. The average room rate of resort B is $143/night. There is always room available in resort B, i.e., the probability of room availability is 100% for resort B.
What would be the expected cost of Co if the inn over-estimates the number of no-shows? 

Solution:

A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season.


A family-run inn has 50 rooms. The inn is considering the use of overbooking, because the frequency of no-shows has left many rooms vacant during the past summer season.


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