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IEMS 313: Foundations of Optimization


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Prerequisites

CS 110, 111, or 150; Gen_Eng 205-1; Math 228-1; sophomore standing

Description

This course examines 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, formulating and solving optimization problems with the AMPL modeling software, and examples in resource allocation, scheduling, operations planning, and transportation.

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