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RollerDice Problem
Decision Models
Review Session 5 1

RollerDice is building a new hotel/casino in Las Vegas. The hotel will have two kinds of
rooms, regular and luxury. They plan to charge $120 per night for regular rooms and $360
per night for luxury rooms.

Based on extensive market research and past-occupancy data, RollerDice believes that the
daily demand for regular rooms will be normally distributed with a mean of 100 and a
standard deviation of 30.

Likewise, the daily demand for luxury rooms will be normally distributed with a mean of 30
and a standard deviation of 5. Furthermore, the demands have a 30% correlation. If demand
for either type of room exceeds the availability, the customer is lost to another hotel.

The demand should be rounded to the nearest non-negative whole number.

RollerDice first wants to evaluate the plan of having 100 regular rooms and 50 luxury rooms.
RollerDice would like to know what its expected profit under this room allocation and also
how likely it is to lose one or more customers.

Now suppose that RollerDice wants to find the number of regular and luxury rooms to build to
maximize the expected revenue. Choose the best policy in the following set of reasonable
room allocations:
90 regular rooms, 55 luxury rooms
100 regular rooms, 50 luxury rooms
110 regular rooms, 45 luxury rooms
120 regular rooms, 40 luxury rooms
Decision Models
Review Session 5 2
RollerDice Demand Description

Based on extensive market research and past-occupancy data, RollerDice
believes that the daily demand for regular rooms will be normally distributed with
a mean of 100 and a standard deviation of 30.

Likewise, the daily demand for luxury rooms will be normally distributed with a
mean of 30 and a standard deviation of 5. Furthermore, the demands have a
30% correlation. If demand for either type of room exceeds the availability, the
customer is lost to another hotel. (None of the customers for regular rooms will
pay for luxury rooms and none of the luxury room customers will want to take a
regular room.)

The demand should be rounded to the nearest non-negative whole number. To
do this use the formula “=ROUND(A1,0)” to transform the fractional demand
value in cell A1, for example, to the nearest non-negative whole number.

RollerDice first wants to evaluate the plan of having 100 regular rooms and 50
luxury rooms. RollerDice would like to know what its expected profit under this
room allocation and also how likely it is to lose one or more customers because
the desired type of room (regular or luxury) is not available.