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SAMPLE MODELS
313
Linearization Option: Construction Cost
Estimation
File name: LINEARZ.XLSX
TYPE: NONLINEAR/LINEAR OPTIMIZATION
Application Profile
This example demonstrates how one might develop a model for estimating construction costs, as well
as performance gains resulting from What’sBest!’s exclusive linearization option. Note, we classify
this model as both nonlinear and linear. As you will see, the model, as formulated, is nonlinear.
However, after invoking the linearization option in What’sBest!, the solver automatically converts this
nonlinear model to an equivalent linear model.
The Problem in Words
You are a contractor specializing in home construction. You have the opportunity to bid on a job that
involves building a number of homes in a new housing development. In order to place an intelligent
bid, you need to calculate your expected cost on a per home basis. Based on past experience, you know
the following three factors primarily determine the construction cost of a house: total square footage,
number of bedrooms, and number of baths.
You believe there is a linear relationship between these three factors and total cost. Specifically, you
have come up with the following equation:
Total Cost = 1+(2*Sq. Feet)+(3*Bedrooms)+(4*Bathrooms)
(i)
You pull up the following historical data from projects your company has completed in the past:
Sq. Feet Beds
1500
1
1600
1
2200
2
2600
3
3000
3
3500
5
4000
4
5200
2
8200
4
8700
6
Baths
1
1
1
2
2
2
4
3
4
4
Objective of Optimization
Cost($000)
78.5
105.8
149.1
173.8
224.4
267.0
302.7
302.0
438.7
490.4
You will use your historical data to estimate values for the beta coefficients 1, 2, 3, and 4) in
formula (i). You want your estimation function to avoid the case where it might be a poor predictor on
one type of home. Thus, you have decided you want your model’s objective to minimize the maximum
error in your cost estimations. Note, that this process of fitting a linear function to a set of data points
is referred to as linear regression.