# Courses  /  DescriptionsIEMS 313: Foundations of Optimization

### Quarter Offered

Fall : MWF 11:00-11:50 (Lab: M 4:00, 5:00) ; Kucukyavuz
Winter : MWF 11:00-11:50 (Lab: M 3:30, 4:30) ; Wilson
Spring : MWF 11:00-11:50 (Lab: M 12:00, 1:00) ; Dowson

### Prerequisites

EECS 111, Gen Eng 205-1, Math 230, Sophomore standing

### Description

Formulation and solution of applicable optimization models, including linear, integer, nonlinear, and network problems. Efficient algorithm methods and use of computer modeling languages and systems.

• This course is a major requirement for Industrial Engineering

LEARNING OBJECTIVES

• Students will know and be able to formulate linear and mixed-integer linear optimization models
• Students will be able to explain the properties of linear optimization models
• Students will know duality and sensitivity analysis and be able to use those concepts to predict What-If scenarios
• Students will know and be able to apply several fundamental optimization algorithms
• Students will be able to model and solve network flow and shortest path problems
• Students will be able to model and solve optimization problems with mathematical optimization software

TOPICS

• Linear programming models
• Simplex algorithm
• Mixed-integer programming models
• Branch-and-bound algorithm
• Duality and sensitivity analysis
• Minimum cost network flow problems and shortest path problems
• Dijkstra’s algorithm
• Short introduction to nonlinear programming

MATERIALS

Recommended:

• Optimization in Operations Research, 2nd ed, Ronald L. Rardin, ISBN-13: 978-0-13-438455-9
• AMPL: A Modeling Language for Mathematical Programing, 2nd ed, Fourer, Gay, & Kernighan, ISBN-13: 978-0-534-38809-6 (also available for free online)

ADDITIONAL INFORMATION

Introduction to mathematical optimization and its applications. Linear optimization models. Simplex Algorithm. Sensitivity analysis. Mixed-integer optimization models.  Branch-and-bound algorithm. Network-flow optimization models.  Nonlinear optimization introduction. Examples in resource allocation, scheduling, operations planning, and transportation. Formulating and solving optimization problems with the AMPL modeling software.

In teams, students work on a project involving the direct application of the concepts learned in the course.