# Hilton Inn Probability and Inventory Control for Overbooking

The Hilton Inn has decided to use good inventory control to decide how many customers to book to the hotel. The hotel has 100 rooms and Hilton Inn charges $120 per night per room. The number of no-shows has the following probability distribution:

Number of no shows Probability

0 0.10

1 0.15

2 0.20

3 0.15

4 0.10

5 0.05

6 0.05

7 0.05

8 0.05

9 0.05

10 0.05

If Hilton Inn overbooks and no room is available, the customer is sent to the Sheraton across the street and the Hilton Inn customers, seeing that this is a nicer hotel, accept this without any protest or requesting any further compensation. Hilton Inn pays the Sheraton $170 for each room they use in an overbooking situation (but keeps the $120 they got from the customer).

Under the above described scenario, how many rooms should Hilton Inn overbook?

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#### Solution Preview

As per the given information, the given problem is a single period stochastic inventory model. The probability distribution of the number of no-shows of overbooking is given. Further, it is given that, Hilton Inn Charge $120 ...

#### Solution Summary

Hilton Inn probability and inventory controls for overbooking hotel rooms are examined.