Texts and References:
R. Fourer, D. Gay and B. Kernighan "AMPL: A Modeling Language for Mathematical Programming", Boyd & Fraser Publishing Company, 1993
The first book is our main text . The second is important for learning AMPL.
We will have a final exam. I will give one partial take-home exam worth 40% of your grade. By partial take-home I mean that the questions will be distributed a few days before the exam date and you will have time to work on them and even collaborate with each other in order to solve them. However on the exam day, you will have to write the answers in your own words closed book and notes, and obviously without any collaborations!
In this course the main purpose is to cover a broad spectrum of topics on linear programming. We cover the basic material such as he simplex method and duality theory. But a healthy part of the course will be devoted to applications and modeling, especially as it is relevant to a business school study. We will also use AMPL or related software for modeling projects. AMPLa modeling language will be used for some modeling projects.
Here are the topics I wish to cover in this course. I intentionally put more stuff than I can possibly cover during the semester, and adjust things as the course evolves, so don't be alarmed! This part will be changed as we go along. I will give details, and exact dates when the material will be covered only for the next few lectures. I may also juggle some of the topics, add new ones and eliminate others as we go along.
Basic simplex algorithm
Read chapters 1 and 2, plus lecture notes
The dual simplex method Read chapter 5, section 6 through 10
Weeks 6 & 7: Matrix notation, the revised simplex method, sensitivity analysis
sensitivity and parametric analysis
Read chapters 6 & 7 plus lecture notes
Weeks 8 & 9 & 10: Implementation issues:
numerical analysis of pivoting: LU factorization and updates, sparse matrices
Read chapter 8
Week 8 & 9 & 10: Network Flows and Network simplex algorithm
Dijkstra's shortest algorithm and dynamic programming
Read chapters 13 and 14 and lecture notes
Week 11: statistical application: regression, stochastic programming
introduction to stochastic programming and linear programming applications
Read chapter 12 and notes
Week 12: Introduction to game theory
some economic applications
Read chapter 11 and lecture notes
Week 13 &14: Introduction to interior point methods
similarities to and differences from the simplex method
Read chapter 16 and 17 and 18