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
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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.
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MPL: Just ignore the message…
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MPL/CPLEX Activating the license
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Acknowledgment from Cplex
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Email from Cplex From [email protected] Thu Feb 24 12:21:30 2005 Date: Thu, 24 Feb 2005 09:16:51 -0800 (PST) From: [email protected] To: [email protected] Subject: License Instructions for MPL and CPLEX Mime-Version: 1.0 Content-Transfer-Encoding: 7bit X-Spam-Checker-Version: SpamAssassin 2.60 (1.212-2003-09-23-exp) on sundial.cs.cornell.edu X-Spam-Status: No, hits=-1.4 required=5.0 tests=BAYES_01,NO_REAL_NAME autolearn=no version=2.60 X-Spam-Level: Dear Carla Gomes, Thank you for registering your copy of MPL and CPLEX provided with the book Hillier and Lieberman, Introduction to Operations Research, Seventh Edition. Instructions for activating your license appear below. If you have any questions or require support, please contact Maximal Software at [email protected] . The steps for activating your license are listed below. Please note the special activation password listed in Step 3. etc
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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)
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MPL: Solution Options
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Checking Syntax and Runnig
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Syntax
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Solving it with Cplex
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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
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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
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Solution File MPL Modeling System - Copyright (c) 1988-2000, Maximal Software, Inc.
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