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335-notes-all

335-notes-all - Lecture Notes for Industrial Engineering...

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Lecture Notes for Industrial Engineering Operations Research – Optimization Spring Professor Nelson Uhan School of Industrial Engineering Purdue University
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Contents Introduction to Optimization Introduction An Introduction to Formulating Optimization Models Trade-o s in Optimization Modeling, Large-Scale Optimization Models Solving Optimization Models Graphically and Outcomes of Optimization Models Classi cation of Optimization Models, Local and Global Optimal Solutions Solving Optimization Models with a Computer – An Introduction to GAMS Linear Optimization Linear Programming Models I Linear Programming Models II Linear Programming Models III e Simplex Method I e Simplex Method II e Simplex Method III e Simplex Method IV e Simplex Method V Introduction to Sensitivity Analysis for Linear Programming Linear Programming Duality I Linear Programming Duality II Sensitivity Analysis for LP – Interpreting Solver Output LP Duality and Game eory i
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ii Industrial Engineering – Spring Interior Point Methods for LP Network Optimization Introduction to Networks and the Shortest Path Problem Longest Paths and Project Scheduling e Maximum Flow Problem Minimum Cost Flows I Minimum Cost Flows II Minimum Cost Flows III Multicommodity Flows and Stable Matchings Discrete Optimization Integer Programming Models I Integer Programming Models II Integer Programming Models III Integer Linear Programs and LP Relaxations Branch and Bound I Branch and Bound II Metaheuristics
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Introduction to Optimization
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Lecture Introduction What is operations research? • “ e most in uential academic discipline eld you’ve never heard of” [Boston Globe, ] Operations Research (OR) is the discipline of applying advanced mathematical methods to help make better decisions • “ e Science of Better” [INFORMS slogan] • “Useful applied math” • “A liberal education in a technological world” [ omas Magnanti, former Dean of Engineering at MIT] • Numerous applications, including manufacturing operating systems logistics airline pricing communications nance marketing • We’ll talk about some applications later • Nice article from the Boston Globe: http://web.ics.purdue.edu/~nuhan/opeverything.html
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Industrial Engineering – Spring e trave ing sa esperson prob em A saleswoman located in Indianapolis wants to visit all state capitals of the continental United States to sell her wares • What is shortest way of visiting all the capitals and then returning to Indianapolis? • Entire books have been written on the TSP : contest by Proctor and Gamble - best TSP tour through US cities : e Florida Sun-Sentinel’s Science page ponders Santa Claus’s traveling problem • One of the most popular problems in operations research • Numerous applications in expected and unexpected places Circuit board manufacturing Genome sequencing • Your turn! Try to nd the shortest way of visiting all the capitals and then returning to Indianapolis
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