The Titan hotel routinely experiences no-shows (people making reservations and not
showing up) during the peak season when the hotel is always full. No-shows follows
the probability distribution given in the table below:
No-shows (x) Probability
0 0.1
1 0.13
2 0.31
3 0.16
4 0.21
5 0.09
In order to lessen the number of vacant rooms, the hotel uses an overbooking policy
through which it accepts three more reservations than the number of rooms
available. On a day when the hotel experiences fewer than three no-shows, there are
not enough rooms for those who have reservations. The hotelAc€?cs policy is to send
these guests to a closely located competing hotel, at a cost, supported by the Titan
hotel, of $125 per person. If the number of no-shows is more than three, the hotel
has vacant rooms, resulting in an opportunity cost of $50 per person.
a. Simulate 3000 days of operation to calculate the hotelAc€?cs average daily cost
due to overbooking and opportunity costs.
b. Determine the optimal number (0, 1, 2, 3, 4, 5, 6) of rooms that the Titan
hotel should overbook in order to minimize average daily costs.
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