Academics / Courses / DescriptionsIEMS 313: Foundations of Optimization
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Prerequisites
CS 110, 111, or 150; Gen_Eng 205-1; Math 228-1; sophomore standingDescription
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.