Zahra_Mohaghegh_Feb26

Zahra_Mohaghegh_Feb26 - Engineering Management & Systems...

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1 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 February 26, 2008
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2 Engineering Management & Systems Engineering The George Washington University Sensitivity Analysis : An Sensitivity Analysis : An Applied Approach Applied Approach
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3 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Defining the Topic ± Changing the Objective Function Coefficients ± Changing the Right Hand Sides ± Shadow Price ± Importance of Sensitivity Analysis ± The Computer and Sensitivity Analysis ± Managerial Use of Shadow Prices
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4 Engineering Management & Systems Engineering The George Washington University Outline Outline ± Defining the Topic ± Changing the Objective Function Coefficients ± Changing the Right Hand Sides ± Shadow Price ± Importance of Sensitivity Analysis ± The Computer and Sensitivity Analysis ± Managerial Use of Shadow Prices
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5 Engineering Management & Systems Engineering The George Washington University What is What is What What - - if analysis if analysis ? ? ± Studies of how changes in the model parameters affect the optimal basis and its associated optimal solution. ± Also called Sensitivity analysis provides a wealth of information to decision makers not only about how robust a solution is, but also about elements with high leverage.
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6 Engineering Management & Systems Engineering The George Washington University Giapetto Giapetto s s Workshop Workshop ± Giapetto’s, Inc., manufactures wooden soldiers and trains. ± Product characteristics: ± Each week Giapetto can obtain: ± All needed raw material. ± Only 100 finishing hours. ± Only 80 carpentry hours. ± Demand for the trains is unlimited. ± At most 40 soldiers are bought each week. ± Exercise: build an LP model to maximize Giapetto’s profit 1 1 Carpentry Labor 1 2 Finishing Hours $10 $14 Cost $9 $10 Raw Materials $21 $27 Selling Price Train Soldier Product\Resources
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7 Engineering Management & Systems Engineering The George Washington University Model Model ± Defining x 1 as the number of soldiers, and x 2 the number of trains, we obtain the following optimization problem. max z = 3x 1 + 2x 2 s.t .2 x 1 + 2 100 1 + 2 80 1 40 1 0 2 0
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8 Engineering Management & Systems Engineering The George Washington University Questions Questions ± Consider the “Giappetto’s Workshop” problem. Giappetto as a decision maker is interested not only on how much trains and soldiers to produce. He might also want to answer questions like: 1. How much does the price of a soldier have to increase to make them more profitable?
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This note was uploaded on 01/02/2010 for the course EMSE 202 taught by Professor Mohaghegh,abeledo during the Spring '07 term at GWU.

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Zahra_Mohaghegh_Feb26 - Engineering Management & Systems...

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