Course Name | Combinatorial Optimization |
Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
---|---|---|---|---|---|
IE 354 | Fall/Spring | 3 | 0 | 3 | 6 |
Prerequisites |
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Course Language | English | ||||||||
Course Type | Elective | ||||||||
Course Level | First Cycle | ||||||||
Mode of Delivery | - | ||||||||
Teaching Methods and Techniques of the Course | |||||||||
Course Coordinator | - | ||||||||
Course Lecturer(s) | - | ||||||||
Assistant(s) | - |
Course Objectives | To introduce the concepts of combinatorics, counting rules, recurrence relations and other topics related with combinatorial optimization. To present the application of these concepts to operational research problems. |
Learning Outcomes | The students who succeeded in this course;
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Course Description | The course covers a broad range of topics in combinatorial modeling and the systematic analysis. The topics include basic counting rules, generating functions, recurrence relations, some famous combinatorial optimization problems and related mathematical techniques. |
Related Sustainable Development Goals | |
| Core Courses | |
Major Area Courses | X | |
Supportive Courses | ||
Media and Managment Skills Courses | ||
Transferable Skill Courses |
Week | Subjects | Required Materials |
1 | What is Combinatorics? | |
2 | Introduction to Counting | Reading the slides supplied by the instructor Inroduction to Basic Counting Rules |
3 | Basic counting rules I | Reading the slides supplied by the instructor Basic Counting Rules |
4 | Basic counting rules II | Reading the slides supplied by the instructor Basic Counting Rules |
5 | Basic counting rules III | Reading the slides supplied by the instructor Basic Counting Rules |
6 | Recurrence relations I | Reading the slides supplied by the instructor Recurrence relations |
7 | Recurrence relations II | Reading the slides supplied by the instructor Recurrence relations |
8 | Midterm Exam | |
9 | Graph Theory I Famous Problems in Combinatorial Optimization I | Reading the slides supplied by the instructor Graph Theory |
10 | Graph Theory II Famous Problems in Combinatorial Optimization II | Reading the slides supplied by the instructor Graph Theory |
11 | Graph Theory III Famous Problems in Combinatorial Optimization III | Reading the slides supplied by the instructor Graph Theory |
12 | Graph Theory IV Famous Problems in Combinatorial Optimization IV | Reading the slides supplied by the instructor Graph Theory |
13 | Computational Complexity, Analysis of algorithms | Reading the slides supplied by the instructor Computational Complexity |
14 | Optimization Methods Famous Problems in Combinatorial Optimization V | Reading the slides supplied by the instructor Optimization Methods |
15 | Midterm Exam | |
16 | Review of the Semester |
Course Notes/Textbooks | Lovasz, Laszlo. Matching Theory. Ahuja, R., T. Magnanti, and J. Orlin. Network Flows. Schrijver, A. Theory of Linear and Integer Programming. Chvatal, V. Linear Programming. Bertsimas, D., and J. Tsitsiklis. Linear Optimization. Cook, W. J., W. H. Cunningham, W. R. Pulleyblank, and A. Schrijver. Combinatorial Optimization. Papadimitriou, C. H., and K. Steiglitz. Combinatorial Optimization. |
Suggested Readings/Materials | Introductory Combinatorics, R.A. Brualdi, Prentice Hall, NJ, 1999 Applied Combinatorics, F.S. Roberts, Prentice Hall, NJ, 1984 Applied Combinatorics, A. Tucker, John Wiley & Sons, NY, 1984 A Friendly Introduction to Graph Theory, F. Buckley and M. Lewinter, Prentice Hall, NJ, 2002 Discrete and Combinatorial Mathematics: An Applied Introduction, Fifth Edition. Ralph P. Grimaldi, Addison Wesley, 2003. Combinatorial Optimization: Algorithms and Complexity, Christos H. Papadimitriou and Kenneth Steiglitz, Dover Publications, 1998. Lecture handouts. |
Semester Activities | Number | Weigthing |
Participation | 1 | 10 |
Laboratory / Application | ||
Field Work | ||
Quizzes / Studio Critiques | ||
Portfolio | ||
Homework / Assignments | 1 | 20 |
Presentation / Jury | ||
Project | ||
Seminar / Workshop | ||
Oral Exam | ||
Midterm | 1 | 30 |
Final Exam | 1 | 40 |
Total |
Weighting of Semester Activities on the Final Grade | 3 | 60 |
Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
Total |
Semester Activities | Number | Duration (Hours) | Workload |
---|---|---|---|
Course Hours (Including exam week: 16 x total hours) | 16 | 3 | 48 |
Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | ||
Study Hours Out of Class | 14 | 3 | 42 |
Field Work | |||
Quizzes / Studio Critiques | |||
Portfolio | |||
Homework / Assignments | 1 | 40 | |
Presentation / Jury | |||
Project | |||
Seminar / Workshop | |||
Oral Exam | |||
Midterms | 1 | 20 | |
Final Exams | 1 | 30 | |
Total | 180 |
# | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
1 | To have adequate knowledge in Mathematics, Science and Industrial Engineering; to be able to use theoretical and applied information in these areas to model and solve Industrial Engineering problems. | X | ||||
2 | To be able to identify, formulate and solve complex Industrial Engineering problems by using state-of-the-art methods, techniques and equipment; to be able to select and apply proper analysis and modeling methods for this purpose. | X | ||||
3 | To be able to analyze a complex system, process, device or product, and to design with realistic limitations to meet the requirements using modern design techniques. | X | ||||
4 | To be able to choose and use the required modern techniques and tools for Industrial Engineering applications; to be able to use information technologies efficiently. | X | ||||
5 | To be able to design and do simulation and/or experiment, collect and analyze data and interpret the results for investigating Industrial Engineering problems and Industrial Engineering related research areas. | |||||
6 | To be able to work efficiently in Industrial Engineering disciplinary and multidisciplinary teams; to be able to work individually. | |||||
7 | To be able to communicate effectively in Turkish, both orally and in writing; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively; to be able to give and receive clear and comprehensible instructions | |||||
8 | To have knowledge about contemporary issues and the global and societal effects of Industrial Engineering practices on health, environment, and safety; to be aware of the legal consequences of Industrial Engineering solutions. | |||||
9 | To be aware of professional and ethical responsibility; to have knowledge of the standards used in Industrial Engineering practice. | |||||
10 | To have knowledge about business life practices such as project management, risk management, and change management; to be aware of entrepreneurship and innovation; to have knowledge about sustainable development. | |||||
11 | To be able to collect data in the area of Industrial Engineering; to be able to communicate with colleagues in a foreign language. | |||||
12 | To be able to speak a second foreign at a medium level of fluency efficiently. | |||||
13 | To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Industrial Engineering. |
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest