mccarl-chapter9

mccarl-chapter9 - Chapter 9 NONLINEARITIES AND...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 9 NONLINEARITIES AND APPROXIMATION.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MAD Models Minimize the sum of absolute deviations • The deviation is defined as ei = Yi - ∑X ji B j Similar to regression, except we minimize sum of the absolute values of the error term and not the sum of the squares of the error terms.
Background image of page 2
Problem Defined Minimize ∑ | ei | Subject to ei - ∑ Xji bj = Yi The bj are the variables to be determined in the model. They can be positive or negative, as can the ei.
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Need Substitutions to solve Define ei = eipos – eineg Define bj = bjpos – bjneg If we replace these in the formulation, we can solve these. Remembering that the absolute value is always a positive number, we have an objective function that sums up over all eipos + eineg.
Background image of page 4
Example from Book Price of Oranges Quantity of Oranges Sold Quantity of Juice Sold 10 8 5 5 9 1 4 10 9 2 13 8 6 15 2 9 17 3 Predict the price based on quantity of oranges and quantity of juice sold.
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Orange Price Model • Price i = Bo + B1QOranges i + B2QJuice i + e i The ei can be positive or negative, as can the Bj. Decision variables are the Bj and the ei which are determined by the choice of the Bj. Because I minimize the sum of absolute values, I must define two error terms for each observation, the positive and the negative.
Background image of page 6
The LP from this Problem e1p e1n e2p e2n e3p e3n e4p e4n e5p e5n e6p e6n b0 b1 b2 min RHS used Obj 1 1 1 1 1 1 1 1 1 1 1 1 11.277 obs 1 1 -1 1 8 5 eq 10 10 2 1 -1 1 9 1 eq 5 5 3 1 -1 1 10 9 eq 4 4 4 1 -1 1 13 8 eq 2 2 5 1 -1 1 15 2 eq 6 6 6 1 -1 1 17 3 eq 9 9 answers 5.79 0 0 0 0 0 0 2.72 0 0 2.77 0 3.43 0.19 -0.15 Here, I've let the Bj be unrestricted in sign, because Solver will let me do that. I could add more columns and define negative Bj.
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Variation Minimize the biggest absolute deviation from the line. This can be accomplished by using inequality
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 32

mccarl-chapter9 - Chapter 9 NONLINEARITIES AND...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online