IE 316: Advanced Operations Research Techniques
Miscellaneous Handouts (PDF Format)
Lecture Slides (PDF Format)
- 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.
- Lecture 9: Finding an Initial Basic Feasible Solution.
- Lecture 10: Modeling Languages.
- Quiz 1 Review.
- Lecture 11: Duality.
- Lecture 12: The Dual Simplex Method.
- Lecture 13: The Recession Cone, Extreme Rays, and Representation of Polyhedra.
- Lecture 14: Local Sensitivity Analysis.
- Lecture 15: Global Sensitivity Analysis.
- Lecture 16: Large-scale Linear Programming.
- Quiz 2 Review.
- Lecture 17: Introduction to Network Flow Problems.
- Lecture 18: The Network Simplex Algorithm.
- Lecture 19: The Negative Cost Cycle Algorithm and Maximum Flows.
- Lecture 20: Assignments, Shortest Paths, and Minimum Spanning Trees.
- Lecture 21: Introduction to Integer Programming.
- Lecture 22: Branch and Bound Methods.
- Lecture 23: Strong Formulations for Integer Programs.
- Lecture 24: Mathematical Programming in Practice.
- Final Review.
AMPL Files Used in Lecture
Assignments (PDF Format)
- Problem Set #1 (due Sept 10)
- Problem Set #2 (due Sept 17)
- Problem Set #3 (due Sept 24)
- Problem Set #4 (due Oct 15)
- Problem Set #5 (due Oct 22)
- Problem Set #6 (due Oct 29)
- Problem Set #7 (due Nov 21)
- Problem Set #8 (due Dec 5)
- Extra Credit (due Dec 5)
Reference Texts
- Course Text: Introduction to Linear Optimization, D. Bertsimas and J. Tsitsiklis, Athena Scientific (1997).
- AMPL: A Modeling Language for Math Programming, R. Fourer, D. M. Gay, and B. W. Kernighan, Duxbury Press (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).
AMPL Pointers
- AMPL Web site
- AMPL Book: Chapter 1
- A Modeling Language for Mathematical Programming
- Submitting AMPL models over the Web
- AMPL in Action (Case Studies using AMPL)
- New Features Page (useful reference)
- List of built-in suffixes
- AMPL/CPLEX Reference Guide
Guides and Pointers on the Web
- 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
- John Mitchell’s Optimization Pointers
On-line Tutorials, Case Studies, and Interactive Optimization
- IFORS tutORial Project
- NEOS Server — solve optimization problems over the Web
- NEOS Case Studies — includes an interactive version of the Diet Problem
- Case studies using AMPL — includes the McDonald’s Diet Problem.
- Math Programming in Action
- Operations Research Models and Methods — a fantastic on-line introduction to OR including Excel add-ins
- On-line MPL Tutorial
- Tutorial on Spreadsheet Optimization
- The Remote Interactive Optimization Testbed (RIOT) Page
- J.E. Beaseley’s OR Notes
- AMPL in Action (Case Studies using AMPL)
- On-line Graphical LP Solver
- NEOS Java Graphical LP Solver
