Zahra_Mohaghegh_Jan22_module 2_EMSE102-202

Zahra_Mohaghegh_Jan2 - Engineering Management Systems Engineering The George Washington University EMSE 102-202 Survey of Operations Research

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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 [email protected] Post-Doctoral Research Associate Center For Risk and Reliability University of Maryland January22, 2008 Module_2
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Engineering Management & Systems Engineering The George Washington University Chapter (3) Chapter (3) Introduction to Linear Programming 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 What is Linear Programming? ± A solution method for complex decision problems faced by many business and government organizations. ± What type of problems? Resource allocation problems where an optimal use of the resources is desired. ± Linear programming is the optimization technique most often used in practice.
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Engineering Management & Systems Engineering The George Washington University Each soldier built: • Yields a net profit of $3. • Requires 2 hours of finishing labor. • Requires 1 hour of carpentry labor. Each train built: • Yields a net profit of $2. • Requires 1 hour of finishing labor. • Requires 1 hour of carpentry labor. Goal : Giapetto wants to maximize weekly profit. A simple example Giapetto’s, Inc., manufactures wooden soldiers and trains toys.
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Engineering Management & Systems Engineering The George Washington University Each week Giapetto can obtain: • All needed raw material. • Only 100 finishing hours. • Only 80 carpentry hours. Additionally: • Demand for the trains is unlimited. • At most 40 soldiers are bought each week. Formulate a mathematical model of Giapetto’s situation that can be used maximize weekly profit.
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Engineering Management & Systems Engineering The George Washington University The Giapetto model has the characteristics shared by all mathematical optimization models. Decision Variables: x 1 = number of soldiers produced each week x 2 = number of trains produced each week Objective Function : Maximize z = 3x 1 + 2x 2 In any linear programming model, the decision maker wants to maximize (usually revenue or profit) or minimize (usually costs) some function of the decision variables.
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Engineering Management & Systems Engineering The George Washington University Constraints : as x 1 and x 2 increase, Giapetto’s objective function grows larger. For Giapetto, the values of x 1 and x 2 are limited by the following three constraints: Constraint 1 Each week, no more than 100 hours of finishing time may be used. Constraint 2 Each week, no more than 80 hours of carpentry time may be used. Constraint 3 Because of limited demand, at most 40 soldiers should be produced. These three constraints can be expressed mathematically by the following linear inequalities: Constraint 1: 2 x 1 + x 2 100 Constraint 2: x 1 + x 2 80 Constraint 3: x 1 40 Any other constraint?
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Engineering Management & Systems Engineering The George Washington University
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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_Jan2 - Engineering Management Systems Engineering The George Washington University EMSE 102-202 Survey of Operations Research

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