GEORGE MASON UNIVERSITY


Department of Systems Engineering and Operations Research

OR 441/MATH 441 - Operations Research I Fall 2005
Thursday 4:30 pm-7:10 pm, KH room 7


Professor Roman A. Polyak

Office: Science and Technology II, Room 127; (703) 993-1685; fax: (703) 993-1521
Office Hours: Tuesday 3:00pm-5:00pm or by appointment; E-mail: rpolyak@gmu.edu
Text:  Wayn .L. Winston, Operations Research Applications and Algorithms, Fourth Edition, Thomson, Brooks/Cole2003.


Course Summary: This course will introduce the basic mathematical ideas and methods of Deterministic Operations Research. We will discuss modeling real life problems, the basic concepts of Linear Programming (LP), and methods for solving LP problems. We are going to discuss briefly some concepts of nonlinear optimization and their applications. There will be homework assignments and a project, which requires modeling real life problems using MPL languages available for downloading from the Internet (www.maximal-usa.com).

 

Grading: 15% homework; 35% midterm exam; 10% computational project; 40% final exam

 

Course Schedule

 

Weeks Topics
1 Introduction to OR. Modeling real life problems.
2 Linear Programming, geometry of LP, basic linear algebra tools for solving LP.
3 Simplex method
4 More on simplex method
5 Sensitivity in LP
6 Duality in LP
7 The transportation problem

8 MIDTERM    (The transportation problem is not on the Midterm)
9 Networks and network optimization
10 Integer and combinatorial optimization
11 Branch and bound method
12 Unconstrained optimization
13 Nonlinear constrained optimization
14 Interior Point Methods in LP
15 Review
FINAL           December 15, 2005

 

This course assumes some knowledge of linear algebra and calculus, which we will review in process of developing the course.

 

 

CLASS NOTES:

 

LECTURE 1

 

LECTURE 2

 

LECTURE 3

 

LECTURE 4

 

LECTURE 5

 

LECTURE 5

 

LECTURE 6

 

LECTURE 7

 

LECTURE 8

 

LECTURE 9

 

LECTURE 10

 

LECTURE 11

 

LECTURE 12