Department of Systems Engineering and Operations Research
OR 441/MATH 441 -
Operations Research I � Fall 2005
Thursday��
Professor Roman A. Polyak
Office: Science
and Technology II, Room 127; (703) 993-1685; fax: (703) 993-1521
Office Hours: Tuesday�
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: