Appendix IB. Course Syllabi

IE 312 Optimization

1. Course Number and Title: IE312, Optimization

2. Course Description:
Concepts, analysis techniques, optimization techniques, and applications of operations research. Construction and optimization of mathematical models for systems using linear programming and goal programming plus post optimality for evaluation results.

3. Prerequisites: Math 266 (Elementary Differential Equations)

4. Textbook:
Optimization in Operations Research by Ronald Rardin, published by Prentice-Hall, 1998, winner if the Institute of Industrial Engineers Book of the Year award in 1998

5. Course Objectives:
In this course, students learn how to

1. formulate mathematical models of complex systems
2. utilize computer software to find solutions of these optimization models
3. apply the concept of improving search by using it for two-variable problems
4. implement the simplex method (and its extensions) for solving linear programs
5. analyze the impact of changes in their linear programming model on the model's solution
6. apply basic techniques for solving specialized types of problems commonly encountered in operations research practice

6. Topics Covered:

1. Introduction and overview of the operations research process
2. Different types of mathematical models
3. Basics of formulating optimization models: decision variables, objective functions & constraints
4. Solving optimization models using the LINDO optimization software
5. Graphical solutions of two-variable problems
6. Categories of optimization models: linear, nonlinear, integer, multi-objective
7. Improving directions and feasible directions
8. Techniques for developing linear programming formulations of real-world systems
9. The simplex algorithm
10. Finding an initial basic feasible solution: the two-phase simplex method
11. Sensitivity analysis: how changes in the model impact its solution
12. Linear programming duality, its economic and mathematical significance
13. Multi-objective optimization & goal programming
14. Finding the shortest path between nodes in a graph
15. Solving network flow (or transshipment) problems
16. Solving transportation & assignment problems
17. Discrete optimization models
18. Basic approaches for solving discrete optimization models

7. Class Schedule:
meets Monday, Wednesday, and Friday from 8:00-8:50 A.M.

8. Contribution of course to meeting the professional component:
Optimization uses mathematical techniques to assist in the solution of real-world problems. Students learn how to formulate complex problems into mathematical models, and identify the appropriate techniques for solving various types of models. Students develop skills in solving optimization problems by using commercial software packages, since these are by far the most common tool for solving such problems in practice. Students also learn how to apply their mathematical knowledge of linear algebra and calculus to solve small problems by hand. Students learn how to interpret the solutions of their mathematical models and how to analyze the impact of changes to the model's parameters and assumptions.

9. Relationship of course to program objectives:

1. Objectives 1, 3, and 6: Optimization techniques are a common tool to assist in managing production and service systems. The techniques used in this course can be applied to a broad range of problems that are relevant in the control of production and service systems.
2. Objectives 2 and 7: Optimization models are often used to quantify trade-offs between various operating goals and requirements. Formulating useful optimization models requires a solid understanding of many aspects of a business. The models developed in this class give students a greater knowledge of the sorts of considerations which are typically of importance.
3. Objectives 1, 2, 3, 6, 7: Mathematical models provide a tool for integrating different aspects of a system by satisfying all of the various requirements at a minimum cost or at a maximum profit.
4. Objectives 3, 5, and 7: Does not directly apply since few non-IE students take this course. However, students do have the opportunity to work on a team project where many of the same principles would apply due to each person's unique talents and perspectives.

10. Person(s) who prepared this description: Tim Van Voorhis, with assistance from Sarah Ryan