Prescriptive Analytics Due
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MSBA7021
Prescriptive Analytics Due
Fall 2022
Assignment 1
1. 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 considerations for multi-site 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 earn-
ings 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 one.
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
In this problem, we will use this regression model together with integer optimization to select the
most profitable sites for La Quinta.
(a) Let us start by understanding the regression equation.
(i) According to the regression equation given above, which variables positively affect Profitabil-
ity? Which variables negatively affect Profitability? Does this intuitively make sense to you?
(ii) La Quinta routinely uses this regression equation to predict Profitability, and to screen poten-
tial real estate acquisitions. Suppose that La Quinta is looking to expand their locations in
California, and has collected data for 16 different potential sites. This data is available in the
file SelectingHotels.csv. For each hotel, we have the location, the price, and the value of each
of the independent variables used in the regression equation. Using the regression equation
and the four normalized independent variables, what is the predicted Profitability of hotel 1?
(iii) Now use the regression equation and the data to compute the predicted Profitability for all
hotels. Which hotel has the highest predicted Profitability? How about the lowest?
(b) La Quinta has a budget of $10 million to spend on hotels. Suppose we used a “greedy” approach
where we selected the most profitable hotels until we ran out of budget. So we would start by
buying the hotel we predict to be the most profitable, and then if we had enough budget left, we
would buy the hotel we predict to be the second most profitable, and so on.
(i) Describe what we would do with this approach. Which hotels would we purchase?
(ii) What would our total predicted Profitability be?
(iii) If we are trying to maximize our total predicted Profitability, is this a good approach? How
about if we were trying to maximize the average predicted Profitability of the hotels we select?