The following table shows observed electrical power consumption at several different
levels of a factory’s operation:
i
Level (`i )
Power (pi )
1
2
3
4
2
3
5
7
1
3
3
5
Engineers want to fit the estimated relationship
power = β0 + β1 ×level
to these data in a way that minimizes the sum of the absolute deviations between
predicted and observed power requirements. Both parameters β0 and β1 should be
nonnegative.
• Formulate an LP to choose the optimal β0 and β1 . Use the method learned in
class for minimizing the sum of absolute values by using a zi upper bound.
• Solve it with AMPL and CPLEX. Hint: the total error is 1.857142857. Draw the
data points, and the fitted line.
1