Syllabus

for MSIS 26:711:651 Linear Programming

Last updated on 9/23/12 at 12:51 PM



Texts and References:

  1. (Required)Vanderbei, Robert J. "Linear Programming: Foundations and Extensions", second editoin Kluwer Academic Publishers, 2000.

  2. (Recommneded) R. Fourer, D. Gay and B. Kernighan "AMPL: A Modeling Language for Mathematical Programming" 2nd edition , Boyd & Fraser Publishing Company, 2002

The first book is our main text . The second is important for learning AMPL, a modeling language for linear and nonlinear programming

Required work

  1. There will be 6 or 7 homework sets during the semester. They will constitute 50% of your final grade. . Also you will not pass this course if you fail to hand in two homework assignments or more regardless of your total score!

  2. We will have a final exam. worth 40% of your grade.

  3. The other 10% is based on class participation, and performance



Our main purpose in this course is to cover a broad spectrum of topics on linear programming. We cover the basic material such as the simplex method and duality theory. But a healthy part of the course will be devoted to the modeling power of linear programming and its applications particularly in Business disciplines such as supply chain, finance, marketting etc. We will also use AMPL or related software for modeling projects. Some linear algebra computations may be done using Matlab or Matlab like languages (such as Octave).

Topics

Below is a list of topic to be covered in the course. Topics with an asterisk * are optional and may be covered at the discretion of the instructor if there is time.

Week 1 & 2: Basics and definitions.

Read chapters 1 and 2, plus lecture notes

Weeks 3&4 &5: Duality, complementary slackness, convex analysis and the dual simplex method

Weeks 6 & 7: Matrix notation, the revised simplex method, sensitivity analysis

Read chapters 6 & 7 plus lecture notes

Week 8 Numerical issues*

Read chapter 8

Weeks 9 & 10: Network Flows and Network simplex algorithm

Read chapters 13 and 14 and lecture notes

Week 11: statistical application: regression, introduction to game theory

Read chapters 11& 12 and notes

Week 12: Introduction to Integer programming


Read chapter 22

Read chapter 11 and lecture notes

Week 13 &14: Introduction to interior point methods*

Read chapter 16 and 17 and 18