OR 541 Operations Research I - SPRING 2005
Monday 4:30 p.m. 7:10 p.m, Robinson Hall  room B205

Professor: Roman A.Polyak
Office: Science and Technology II, Room 127;
Tel:      (703) 993-1685;
Fax :    ( 703) 993-1521
email:   rpolyak@gmu.edu
Office  Hours: Monday  4:00 p.m. 6:00 p.m. or by appointment.

Texts: Wayne.L.Winston, Operations Research Applications and Algorithms, Fourth Edition, Thomson, Brooks/Cole 2003.

Course Summary:  

In the introduction we discuss real life applications, which led to linear (LP) and nonlinear(NLP) optimization problems.
In the first part of the course we will concentrate on the basic concepts and algorithms for LP. It includes Simplex Method, Duality and Sensitivity Analysis. The role of pricing in real life applications will be particularly emphasized. In the second part of the course we will discuss network optimization problems including Classical Transportation, Shortest Path and Max. Flow. Applications, which lead to Integer LP, will be discussed along with the Branch and Bounds Method for solving Integer LP. We conclude the course by discussing some basic NLP concepts. It will be home work assignments. Computational project will be offered. It requires modeling real life problem and using one of the three modeling languages: GAMS (General Algebraic Modeling System), student version is available at www.amazon.com., MPL available at www.maximal-usa.com. AMPL (A Mathematical Modeling Language), student version is available at www.amazon.com


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

Course Schedule:

Weeks  Topics
1       Introduction
2       Linear Programming Models
3       Simplex Method
4       More on Simplex Method
5       Sensitivity Analysis
6       Duality
7       Transportation problems
10     Network Models
11     Integer programming: modeling and algorithms
12     Nonlinear Programming: models
13     Optimality Criteria and some methods for solving Nonlinear programming problems
14     Basic Concepts of Interior Point Methods in LP
15     Review
16     FINAL EXAM -- May 11th ,2005

This course assumes some knowledge of Linear Algebra and Calculus, which we will review in process of developing the course.