Zahra_Mohaghegh_Jan29_module 2_P

Zahra_Mohaghegh_Jan29_module 2_P - Engineering Management...

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Engineering Management & Systems Engineering The George Washington University EMSE 102 EMSE 102 - - 202 202 Survey of Operations Research Methods Survey of Operations Research Methods Zahra Mohaghegh mohagheg@umd.edu Post-Doctoral Research Associate Center For Risk and Reliability University of Maryland January29, 2008 Module_2
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Engineering Management & Systems Engineering The George Washington University Simplex Algorithm Simplex Algorithm CREDITS: PARTS OF THIS LECTURE HAVE BEEN DEVELOPED BY PROFESSORS ABELEDO AND CAMPOS-NONEZ
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Engineering Management & Systems Engineering The George Washington University Motivation Motivation Although powerful / easy to use software is available, it is important to understand how algorithms work. The study of algorithms is fundamental for the field of Operations Research
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Engineering Management & Systems Engineering The George Washington University Outline Outline ± How simplex algorithm can be used to find optimal solutions to LPs: ± Standard Form LP ± The Rationale of the Simplex Algorithm ± The Simplex Algorithm ± Alternative Optimal Solutions ± Unbounded Problems / Multiple optimal solutions ± How two computer packages (LINDO & LINGO) can be used to solve LPs ± Explaining how the information on the outputs of the software is related to the discussion of simplex algorithm
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Engineering Management & Systems Engineering The George Washington University Why Simplex Algorithm? Why Simplex Algorithm? ± Graphical solutions for LPs (Discussed in chapter 3) ± only for two-variable linear programming ± Simplex Algorithm ± To solve LPs with more than two variables ( even applicable for many large industrial problem with thousands of variables)
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Engineering Management & Systems Engineering The George Washington University Outline Outline ± How simplex algorithm can be used to find optimal solutions to LPs: ± Standard Form LP ± The Rationale of the Simplex Algorithm ± The Simplex Algorithm ± Alternative Optimal Solutions ± Unbounded Problems / Multiple optimal solutions ± How two computer packages (LINDO & LINGO) can be used to solve LPs ± Explaining how the information on the outputs of the software is related to the discussion of simplex algorithm
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Engineering Management & Systems Engineering The George Washington University The Need for a Standard Form LP The Need for a Standard Form LP ± Before the simplex algorithm can be used to solve an LP, the LP must be converted into a standard form . ± All LP formulations can be modified so that they conform to the standard form.
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Engineering Management & Systems Engineering The George Washington University Linear Programs in Standard Form Linear Programs in Standard Form We say that a linear program is in standard form if the following are all true: 1. Non-negativity constraints for all variables.
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Zahra_Mohaghegh_Jan29_module 2_P - Engineering Management...

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