IEMS 313: Foundations of Optimization

Quarter Offered

Fall : MWF 11:00-11:50 AM (Lab: M 3:00, 4:00 PM) ; Kucukyavuz
Winter : MWF 10:00-10:50 AM (Lab: M 3:00, 4:00 PM) ; Waechter
Spring : MWF 10:00-10:50 AM (Lab: M 2:00, 3:00 PM) ; Nocedal


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


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


  • 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


  • 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



  • 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)


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.