Ted Ralphs

Miscellaneous Handouts and Course Information

• Course Syllabus
• Course Calendar (Google)
• Course Survey
• Quiz 1 Sample Problems
• Quiz 2 Sample Problems
• Final Exam Sample Problems

Lecture Slides

• Introduction
• Lecture 1: What is Mathematical Programming?
• Lecture 2: Examples of Mathematical Programs
• Lecture 3: The Geometry of Linear Programming
• Lecture 4: Basic Solutions and Bases
• Lecture 5: Extreme Points and Optimality
• Lecture 6: Iterative Search Algorithms and the Simplex Method
• Lecture 7: The Revised Simplex Method
• Lecture 8: The Tableau Method and Finding an Initial BFS
• Lecture 9: Modeling Languages
• Lecture 10: Duality
• Lecture 11: The Dual Simplex Method
• Lecture 12: The Recession Cone, Extreme Rays, and Representation of Polyhedra
• Lecture 13: Local Sensitivity Analysis
• Lecture 14: Global Sensitivity Analysis
• Lecture 15: Large-scale Linear Programming
• Lecture 16: Introduction to Network Flow Problems
• Lecture 17: The Network Simplex Algorithm
• Lecture 18: The Negative Cost Cycle Algorithm and Maximum Flows.
• Lecture 19: The Assignment Problem, Shortest Paths, and the Primal-Dual Algorithm.
• Lecture 20: Introduction to Integer Programming.
• Lecture 21: Branch and Bound Methods.
• Lecture 22: Mathematical Programming in Practice.
• Quiz 1 Review
• Quiz 2 Review
• Final Review

Files Used in Lecture

• diet_problem.xls
• simple.mod
• prod.mod
• prod1.dat
• prod2.dat
• mmprod.mod
• mmprod.dat
• manuf.mod

Assignments

• Problem Set #1
• Problem Set #2
• Problem Set #3
• Problem Set #4
• Problem Set #5
• Problem Set #6
• Problem Set #7
• Problem Set #8
• Problem Set #9

Reference Texts

• Course Text: Introduction to Linear Optimization, D. Bertsimas and J. Tsitsiklis, Athena Scientific (1997).
• Linear Programming and Network Flows, M.S. Bazaraa, J.J. Jarvis, and H.D. Sherali, Wiley (1990).
• Optimization in Operations Research, R.L. Rardin, Prentice Hall (1997).
• Introduction to Mathematical Programming, W.L. Winston and M. Venkataramanan, Duxbury Press (2002).
• AMPL: A Modeling Language for Math Programming, R. Fourer, D. M. Gay, and B. W. Kernighan, Duxbury Press (1999).
• Operations Research Models and Methods, P. Jensen — a fantastic on-line introduction to OR including Excel add-ins.
• Model Building in Mathematical Programming, H.P. Williams, Wiley (1999).
• How to Read and Do Proofs: An Introduction to Mathematical Thought Processes, Daniel Solow, Wiley (2001).
• How to Prove It: A Structured Approach, Daniel Velleman, Cambridge University Press (1994).
• Introduction to Mathematical Structures and Proofs, L.J. Gerstein, Springer (1997).

AMPL Pointers

• AMPL Web site
• AMPL Book: Chapter 1
• A Modeling Language for Mathematical Programming
• Submitting AMPL models over the Web
• Examples using AMPL — includes the McDonald’s Diet Problem
• AMPL in Action (Case Studies using AMPL)
• New Features Page (useful reference)
• List of built-in suffixes
• AMPL/CPLEX Reference Guide

Tutorials and Guides

• What is Operations Research? — The Bureau of Labor Statistics’ over view of this career field
• INFORMS Web site — the professional society for Operations Research and Management Science (OR/MS)
• INFORMS News Room — lots of information about OR/MS
• The INFORMS OR/MS Resource Collection — an extensive collection of OR links
• INFORMS Student Union — INFORMS resources for students
• The World of Operations Research and Management Science
• Math World — an amazing on-line mathematics encyclopedia.
• The INFORMS OR/MS Resource Collection — an extensive collection of OR links
• NEOS Guide — a good overview of optimization
• e-Optimization.com
• Harvey Greenburg’s Courseware Page
• Harvey Greenburg’s Mathematical Programming Glossary
• Guide to Optimization Software
• IFORS tutORial Project
• The Traveling Salesman Problem — a page devoted to the world’s best-known optimization problem
• J.E. Beaseley’s OR Notes

Interactive Optimization

• NEOS Server — solve optimization problems over the Web
• NEOS Case Studies — includes an interactive version of the Diet Problem
• Tutorial on Spreadsheet Optimization
• The Remote Interactive Optimization Testbed (RIOT) Page
• NEOS Java Graphical LP Solver
• LP exlorer — 2 dimensional linear programs
• List of Java Applets at the INFORMS Resources site

Case Studies

• Math Programming in Action
• Cap Gemini Enrst and Young Case Studies Database
• LINDO Model Library
• Application Showcase at e-optimization.com
• Facility location case study
• NEOS Case Studies — includes an interactive version of the Diet Problem

List of Pointers to More Sites

• Introduction to Optimization course at MIT — lots of good pointers to sites about optimization.
• OR/MS pointers at OpsResearch.com
• Yahoo’s Operations Research page
• John Mitchell’s optimization pointers
• Kevin Wayne’s OR/CS links