## 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

1. Introduction to Operations Research and Mathematical Modeling
2. 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
3. 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
4. Solving Goal Programming formulations
5. Solving Integer Programming formulations: the Branch \& Bound method
6. Introduction to Non-linear optimization
7. ``What-if'' and sensitivity analysis for LP problems
8. Special LP structures:
• Transportation problems
• Transportation simplex
• Max and Optimal (min-cost) flow problems
9. 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.
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.