Many manufacturing situations, such as the production of large and complex items as aircraft or machines, exhibit a learning effect in which the production time per unit decreases as more units are produced. This is often modeled by a power curve y = ax -b, where a and b are constants. Suppose that data on production times for the first 10 units produced were collected from a new project:
Unit Production Hours
1 ……………………………3,161
2 ……………………………2,720
3 ……………………………2,615
4 ……………………………2,278
5 ……………………………2,028
6 ……………………………2,193
7 ……………………………2,249
8 ……………………………2,268
9 ……………………………1,994
10 …………………………..2,000
a. Develop a model for estimating the power curve to minimize the sum of the squared deviations of the errors. Use nonlinear optimization to find the parameters.
b. Modify your model in part (a) to minimize the sum of the absolute deviations of errors. Use Evolutionary Solver to find the best parameters.