This course studies properties and solution methods for fundamental optimization models, which include Linear Programming, Quadratic Programming, Nonlinear Programming, Network Programming and Combinatorial Optimization Problems.
The technology of operations research is useful to do decision making for various problems in management sciences. Knowledge and ability acquired through this course will help students to solve real optimization problems in the future.
By the end of this course, students will be able to:
・Understand fundamental properties of linear programming and use the simplex method.
・Understand fundamental properties of nonlinear programming and use the steepest descent method and the Newton method.
・Understand fundamental properties of network programming problems and use its solution methods.
・Understand fundamental properties of Knapsack problems and use the branch and bound method.
Linear programming, Nonlinear programming, Network programming, Combinatorial optimization
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
---|---|---|---|---|
- | - | ✔ | - | ✔ |
Attendance is taken in every class.
Students are required to read the text before coming to class.
Course schedule | Required learning | |
---|---|---|
Class 1 | intoroduction to operations research and lienar programming | |
Class 2 | linear programming: dual problem and dual theory for linear programming | |
Class 3 | Test level of understanding with exercise problems and summary of thefirst part of the course. -Solve exercise problems covering the contents of classes 1–2 | Test level of understanding and self-evaluate achievement for classes 1–2. |
Class 4 | the simplex method for linear programming | |
Class 5 | the two-phase simplex method for linear programming | |
Class 6 | Test level of understanding with exercise problems and summary of thefirst part of the course. -Solve exercise problems covering the contents of classes 4-5 | Test level of understanding and self-evaluate achievement for classes 4–5. |
Class 7 | nonlinear programming: case of one variable | |
Class 8 | nonlinear programming: case of multi variables | |
Class 9 | Test level of understanding with exercise problems and summary of thefirst part of the course. -Solve exercise problems covering the contents of classes 7-8 | Test level of understanding and self-evaluate achievement for classes 7-8. |
Class 10 | network programming: transportation problem | |
Class 11 | network programming: shortest path problem | |
Class 12 | Test level of understanding with exercise problems and summary of thefirst part of the course. -Solve exercise problems covering the contents of classes 10-11 | Test level of understanding and self-evaluate achievement for classes 10-11. |
Class 13 | combinatorial optimization: knapsack problem | |
Class 14 | combinatorial optimization: branch and bound method | |
Class 15 | Test level of understanding with exercise problems and summary of thefirst part of the course. -Solve exercise problems covering the contents of classes 13-14 | Test level of understanding and self-evaluate achievement for classes 13-14. |
None required
Course materials can be found on OCW-i
Students will be assessed on their understanding of linear programming, nonlinear programming, network programming, and combinatorial optimization, and their ability to apply them to solve problems.
Students' course scores are based on midterm and final exams (70%) and exercise problems (30%).
No prerequisites