ISyE 3231 Deterministic Operations Research (Summer '99)

Instructor: Spyros Reveliotis
Room #: ISYE 316
Phone #: 894-6608
e-mail: spyros@isye.gatech.edu
Office Hours: 2:00 - 3:00pm TU,TH (or by appointment)

Course Objective

This course is an introduction to Deterministic Operations Research with emphasis on Linear Programming . During the class lectures, emphasis will be placed on

the modeling and analysis of engineering and management problems by means of the above paradigm, and
the analytical techniques (algorithms) for the solution of these problems.

A third objective of the course is to expose the student to existing computational environments / packages that implement the theoretical results / algorithms. However, this objective will be primarily pursued through the homework assignments.

Course Outline

Introduction to Operations Research and Mathematical Modeling
Deterministic OR models:
- Linear Programming (LP) formulations
- Integer Programming (IP) formulations
- Non-linear Programming (NLP) formulations
- Multi-criteria decision making models: Goal Programming (GP) formulations
Solving Linear Programming formulations
- Graphical Solution of 2-var LP's
- Generalization to the n-var case, algebraic characterizations and the fundamental theorem of LP
- The Simplex algorithm
Solving Goal Programming formulations
Solving Integer Programming formulations: the Branch \& Bound method
Introduction to Non-linear optimization
``What-if'' and sensitivity analysis for LP problems
Special LP structures:
- Transportation problems
- Transportation simplex
- Max and Optimal (min-cost) flow problems
Duality theory (time permitting...)

Course Policies

Homework Approximately one per week. It will consist of theoretical problems and/or computing assignments. Collaboration towards the solution of the homework is allowed; however, each student must turn in his/her own work (photocopies will not be accepted). Homework must be turned in on the specified due date.
Exams All exams will be closed books, with only 2 pages of notes allowed. Furthermore, it is expected that your Academic Honor Code will be respected.
Grading
1. Homework: 25%
2. Midterm : 30% (Tentative date: July 8 or 13)
3. Final: 45% (Date: TBA)
Incompletes will be restricted only to very critical (unavoidable) situations, and will be issued only after substantial evidence is provided.
Course GTA's will be available in the undergraduate lab.

Course reading material

Textbook W. L. Winston, Introduction to Mathematical Programming: Applications and Algorithms, 2nd ed., Duxbury Press
Reading supplements to be provided in class
Other useful references (on reserve)
1. Rardin, R. L., Optimization in Operations Research , Prentice Hall
2. Hillier, F.S. & Lieberman, G.J., Introduction to Operations Research , McGraw Hill (5th Ed.)
3. Phillips, D.T., Ravindran, A., & Solberg, J.J., Operations Research: Principles and Practice, John Wiley & Sons, (2nd Ed.)
4. Lawrence, J. A., Jr. & Pasternack, B. A., Applied Management Science, John Wiley & Sons
5. Luenberger, D.G., Linear and Nonlinear Programming, Addison Wesley (2nd Ed.)
6. Bazaraa, M.S., Jarvis, J.J., & Sherali, H.D., Linear Programming and Network Flows, John Wiley & Sons, (2nd Ed.)
The last two books cited above are for those that might like something more challenging!