SIE 440 - Survey of Optimization Methods

SIE 440/540 - Survey of Optimization Methods (3) Survey of methods including network flows, integer programming, nonlinear programming, and dynamic programming. Model development and solution algorithms are covered. 3ES. P, 340.

Winston, W.L., Introduction to Mathematical Programming (2nd ed.), Duxbury Press, 1995.

References: None

J. L. Higle, Associate Professor of Systems and Industrial Engineering

1. Linear programming models
2. Duality theory
3. Simplex algorithm.

On the first day of class, an assignment designed to test facility with prerequisite material is distributed. Results are evaluated and the instructor consults with individual students, if necessary.

This course provides a survey of optimization models and methods. Particular emphasis will be placed on network flow problems, dynamic programming models, integer programs, and nonlinear programs. The objective of this course is the development and application of a variety of mathematical programming methodologies within a number of potential application areas. Due to its "survey" nature, this course is not appropriate for those students desiring an in-depth presentation of the various methodologies covered.

1. Be able to draw upon a variety of mathematical programming modeling approaches when faced with an optimization problem.
2. Be able to suggest and implement solution procedures for such problems.

1. Linear Programming Review: Formulations, duality, complimentary slackness (6 classes)
2. Network Flow Models: Formulations (transportation and general network models), network simplex, other network based problems (12 classes).
3. Dynamic Programming: DP "approach", recursive formulation, resource allocation, equipment replacement (9 classes).
4. Integer Programming: Formulation, branch and bound, implicit enumeration (12 classes)

Class Requirements:

1. Three lecture sessions per week.
2. Approximately seven homework assignments
3. Two midterm examinations
4. Final examination

Student will use mathematical programming software, such as LINDO, LINGO, and GINO to explore solution techniques.

Laboratory Projects: None

1. Homework - 25%
2. Two midterm examinations - 25% each
3. Final examination - 25%

Contribution to professional component:

Contribution to program objectives: Goals

Prepared by: J. L. Higle   Date: April 14, 1998