**OR 541 – Operations Research I - SPRING 2006**

Tuesday

**Professor: Roman A.Polyak**

**Texts**: *Wayne.L.Winston*** ,
Operations Research Applications and Algorithms, Fourth Edition**,

**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

8 SPRING BREAK

9** MIDTERM EXAM**

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 9 th
,2006

Prereq : MATH 203 or equivalent

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