Hanson Inn is a 96-room hotel located near the airport and convention center in Louisville, Kentucky. When a convention or a special event is in town, Hanson increases its normal room rates and takes reservations based on a revenue management system. The Classic Corvette Owners Association scheduled its annual convention in Louisville for the first weekend in June. Hanson Inn agreed to make at least 50% of its rooms available for con- vention attendees at a special convention rate in order to be listed as a recommended hotel for the convention. Although the majority of attendees at the annual meeting typically re- quest a Friday and Saturday two-night package, some attendees may select a Friday night only or a Saturday night only reservation. Customers not attending the convention may also request a Friday and Saturday two-night package, or make a Friday night only or Sat- urday night only reservation. Thus, six types of reservations are possible: Convention customers/two-night package; convention customers/Friday night only; convention cus- tomers/Saturday night only; regular customers/two-night package; regular customers/ Friday night only; and regular customers/Saturday night only. The cost for each type of reservation is shown here:
|
|
Two-NightPackage
|
Friday Night Only
|
Saturday Night Only
|
|
Convention
|
$225
|
$123
|
$130
|
|
Regular
|
$295
|
$146
|
$152
|
|
The anticipated demand for each type of reservation is as follows:
|
|
|
Two-Night
|
Friday Night
|
Saturday Night
|
|
|
Package
|
Only
|
Only
|
|
Convention
|
40
|
20
|
15
|
|
Regular
|
20
|
30
|
25
|
Hanson Inn would like to determine how many rooms to make available for each type of reservation in order to maximize total revenue.
a. Define the decision variables and state the objective function.
b. Formulate a linear programming model for this revenue management application.
c. What are the optimal allocation and the anticipated total revenue?
d. Suppose that one week before the convention, the number of regular customers/ Saturday night only rooms that were made available sell out. If another nonconvention customer calls and requests a Saturday night only room, what is the value of accept- ing this additional reservation?
TABLE 5.11 RETURNS OVER FIVE 1-YEAR PERIODS FOR SIX MUTUAL FUNDS
|
Mutual Funds
Large-Cap Stock
|
Year 1
35.3
|
Year 2
20.0
|
Year 3
28.3
|
Year 4
10.4
|
Year 5
-9.3
|
|
Mid-Cap Stock
|
32.3
|
23.2
|
-0.9
|
49.3
|
-22.8
|
|
Small-Cap Stock
|
20.8
|
22.5
|
6.0
|
33.3
|
6.1
|
|
Energy/Resources Sector
|
25.3
|
33.9
|
-20.5
|
20.9
|
-2.5
|
|
Health Sector
|
49.1
|
5.5
|
29.7
|
77.7
|
-24.9
|
|
Technology Sector
|
46.2
|
21.7
|
45.7
|
93.1
|
-20.1
|
|
Real Estate Sector
|
20.5
|
44.0
|
-21.1
|
2.6
|
5.1
|