4120_lecture8

# 4120_lecture8 - Computational Methods for Management and...

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Computational Methods for Management and Economics Carla Gomes Lecture 8 Reading: 3.6-3.8 of textbook

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Outline Displaying and Solving LP Models on a Spreadsheet and Modeling Languages Introduction to Simples
Solving Large Linear Programming Models

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Modeling Languages A mathematical language that has been designed to efficiently formulate large mathematical models (with thousand of variables/constraints). Examples of modeling languages: AMPL; MPL; GAMS; LINGO. Textbook (CD-ROM): MPL (student version; also from www.maximalsoftware.com) It provides an interface to to Excel (importing and exporting Excel ranges) Powerful state-of-the-art LP based solver CPLEX LINDO (also available from www.lindo.com) LINDO (Traditional optimizer) What’s Best – spreadsheet optimizer LINGO (Linear and Non-liner programming) Formulations in MPL, LINGO, LINDO and What’s best for all the examples in the book.
MPL: Just ignore the message…

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MPL/CPLEX Activating the license
Acknowledgment from Cplex

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MPL

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MPL TITLE WyndorGlass; MODEL MAX Z = 3 X1 + 5 X2; SUBJECT TO X1 <= 4; 2 X2 <= 12; 3 X1 + 2 X2 <= 18; END Note: default assumption – non-negativity constraints (can be changed)
MPL: Solution Options

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Checking Syntax and Runnig
Syntax

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Solving it with Cplex
Optimal Solution

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MPL Modeling System - Copyright (c) 1988-2008, Maximal Software, Inc. -------------------------------------------------------------------------------- MODEL STATISTICS Problem name: WyndorGlass Filename: wyndor.mpl Date: February 25, 2008 Time: 20:07 Parsing time: 0.00 sec Solver name: CPLEX (11.0.0) Objective value: 36.0000000000 Iterations: 2 Solution time: 0.48 sec Result code: 1 Constraints: 3 Variables: 2 Nonzeros: 4 Density: 67 % SOLUTION RESULT Optimal solution found MAX Z = 36.0000 DECISION VARIABLES
PLAIN VARIABLES Variable Name Activity Reduced Cost ------------------------------------------------------ C1 2.0000 0.0000 C2 6.0000 0.0000 ------------------------------------------------------ CONSTRAINTS PLAIN CONSTRAINTS Constraint Name Slack Shadow Price ------------------------------------------------------ R1 2.0000 0.0000 R2 0.0000 1.5000 R3 0.0000 1.0000 ------------------------------------------------------

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RANGES OBJECTIVE PLAIN VARIABLES Variable Name Coefficient Lower Range Upper Range ----------------------------------------------------------------------- C1 3.0000 0.0000 7.5000 C2 5.0000 2.0000 1E+020 ----------------------------------------------------------------------- RANGES RHS PLAIN CONSTRAINTS Constraint Name RHS Value Lower Bound Upper Bound ----------------------------------------------------------------------- R1 4.0000 2.0000 1E+020 R2 12.0000 6.0000 18.0000 R3 18.0000 12.0000 24.0000 ----------------------------------------------------------------------- END
Solution File MPL Modeling System - Copyright (c) 1988-2000, Maximal Software, Inc.

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