Syllabus for MSIS 683: Introduction to linear Programming

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Texts and References:
  1. Vanderbei, Robert J. "Linear Programming:  Foundations and Extensions", Kluwer Academic Publishers, 1996
  2. 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, though not required , is important to learn AMPL.

Required work

  1. Every student should serve as scribe two or three times during the semester. The scribe will be in charge of a particular lecture, and should take notes carefully. These notes then should be transcribed into an MS WORD   document and e-mailed back to me so that I post them in the page. The notes should be sent to me no later than one week after the lecture! The scribing duties will be 10% of your grade. I will do minimal or no editing of your notes so please be careful and precise. Your scribing grade will be subjective and based on my evaluation of your notes.
  2. I will assign 5 or 6 homework sets during the semester. These will constitute 50% of your final grade. The homeworks are due on the day they are assigned at the beginning of the lecture. Homeworks handed out during or after the lecture are considered late. You will lose 25% of the grade for each late homework. No late homework will be accepted after it was graded and handed back. Also you will not pass this course if you fail to hand in two homework assignments or more regardless of your total score!
  3. We will not have any final exam. Instead I will give one partial take-home exam  worth 20% 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. AMPL  a modeling language will  be used for some modeling projects.

Topics

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.
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

Weeks 8 & 9 & 10: Implementation issues:

Read chapter 8

Week 8 & 9 & 10: Network Flows and Network simplex algorithm

Read chapters 13 and 14 and lecture notes

Week 11: statistical application:   regression, stochastic programming

Read chapter 12 and notes

Week 12: Introduction to game theory

Read chapter 11 and lecture notes

Week 13 &14: Introduction to interior point methods

Read chapter 16 and 17 and 18