In: Operations Management
Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows:
Rental Class
Room Super Saver Deluxe Business
Type I $32 $43 —
Type II $17 $35 $39
Type I rooms do not have wireless Internet access and are not available for the Business rental class.
Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 120 rentals in the Super Saver class, 70 rentals in the Deluxe class, and 55 rentals in the Business class. Round Tree has 105 Type I rooms and 120 Type II rooms.
Use linear programming to determine how many reservations to
accept in each rental class and how the reservations should be
allocated to room types.
Variable# of reservations
Supersaver rentals allocated to room type I ?
Supersaver rentals allocated to room type II ?
Deluxe rentals allocated to room type I ?
Deluxe rentals allocated to room type II ?
Business rentals allocated to room type II ?
Is the demand by any rental class not satisfied?
Explain.
How many reservations can be accommodated in each rental class?
Rental Class# of reservations
Supersaver ?
Deluxe ?
Business ?
Management is considering offering a free breakfast to anyone
upgrading from a Super Saver reservation to Deluxe class. If the
cost of the breakfast to Round Tree is $5, should this incentive be
offered?
With a little work, an unused office area could be converted to a
rental room. If the conversion cost is the same for both types of
rooms, would you recommend converting the office to a Type I or a
Type II room?
Why?
Could the linear programming model be modified to plan for the
allocation of rental demand for the next night?
What information would be needed and how would the model
change?
\
>>
Supersaver rentals allocated to room type I =100
Supersaver rentals allocated to room type II =0
Deluxe rentals allocated to room type I = 5
Deluxe rentals allocated to room type II =65
Business rentals allocated to room type II =55
>>>
Demand of Super saver class is not satisfied
>>>
Reservations made in each rental class
Supersaver = 100
Deluxe =70
Business = 55
>>>
Shadow price deluxe type is $11
Shadow price >$5.
Therefore, up gradation must be done
>>>
Shadow price of type I = $32
Shadow price of type II = $24
Shadow price is higher for type I room. Therefore, type I room is recommended
>>>>
Further information required is
>> On an average how many days a person stays in each type of room
>> Demand of various rooms over next few days