La Quinta Motor Inns is a mid-sized hotel chain headquartered in San Antonio, Texas. They are looking to expand to more locations, and know that selecting good sites is crucial to a hotel chain’s success. Of the four major marketing considerations (price, product, promotion, and location), location has been shown to be one of the most important for multisite firms.
Hotel chain owners who can pick good sites quickly have a distinct competitive advantage, since they are competing against other chains for the same sites. La Quinta used data on 57 existing inn locations to build a linear regression model to predict “Profitability”, computed as the operating margin, or earnings before interest and taxes divided by total revenue. They tried many independent variables, such as “Number of hotel rooms in the vicinity” and “Age of the Inn”. All independent variables were normalized to have mean zero and standard deviation 1.
The final regression model is given by:
Profitability = 39.05 - 5.41(State Population per Inn) + 5.86(Price of the Inn) - 3.09(Square Root of the Median Income of the Area) + 1.75(College Students in the Area)
The R2 of the model is 0.51.
In this problem, we’ll use this regression model together with integer optimization to select the most profitable sites for La Quinta.
The solution can be found at:
https://github.com/ssindw/MITAnalyticsEdge/blob/master/9IntegerProgramming/SelectingHotels.xlsx
Schedule a sports tounament with 4 teams - Atlanta, Boston, Chicago and Detroit. These teams are divided into 2 divisions, A and B. Atlanta and Boston are in division 1, while, Chicago and Detroit are in division 2. Each team plays 1 game per weak for a total of 4 weeks.
During the 4 weeks: Each team plays the other team in its division twice. Each team plays teams in other divisions once.
The team with the most wins from each division will play in the championship. For this reason, teams prefer to play divisional games later.
In this problem, we’ll use integer optimization to maximize team preferences. (divisional games later.)
The solution can be found at:
https://github.com/ssindw/MITAnalyticsEdge/blob/master/9IntegerProgramming/SportsScheduling.xlsx