GRADUATE SCHOOL

M.SC. In Industrial Engineering (With Thesis)

IE 510 | Course Introduction and Application Information

Course Name
Discrete Optimization
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
IE 510
Fall/Spring
3
0
3
7.5

Prerequisites
None
Course Language
English
Course Type
Elective
Course Level
Second Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course -
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives Purpose of this course is to give the students an understanding and experience about discrete optimizaton problems, related concepts and exact and approximate solution techniques.
Learning Outcomes The students who succeeded in this course;
  • Be able to develop a fundamental understanding of integer and combinatorial optimization problems
  • Be able to acquire modelling capabilities with binary and integer variables
  • Be able to use advanced modeling tools to formulate and solve complicated real-life optimization problems
  • Be able to analyze various optimization formulations in terms of their strength and learn ways to strengthen a weak formulation
  • Be able to apply various algorithms to solve integer and combinatorial optimization problems
Course Description Formulation of integer and combinatorial optimization problems. Optimality conditions and relaxation. Polyhedral theory and integer polyhedra. Computational complexity. The theory of valid inequality, strong formulations. Duality and relaxation of integer programming problems. General and special purpose algorithms including branch and bound, decomposition, and cutting-plane algorithms.

 



Course Category

Core Courses
Major Area Courses
X
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Introduction
2 Optimality, Relaxation and Bounds
3 Optimality, Relaxation and Bounds
4 Well-solved Cases: Network Flows, Shortest Path, Optimal Trees, Matching and Assignments
5 Well-solved Cases: Network Flows, Shortest Path, Optimal Trees, Matching and Assignments
6 Branch and Bound Methods
7 Branch and Bound Methods
8 Midterm exam
9 Cutting Plane Algorithms: Valid Inequalities, Theory and Practice
10 Cutting Plane Algorithms: Valid Inequalities, Theory and Practice
11 Cutting Plane Algorithms: Valid Inequalities, Theory and Practice
12 Dynamic Programming
13 Approximation Algorithms
14 Approximation Algorithms
15 General Review and Evaluation
16 General Review and Evaluation

 

Course Notes/Textbooks Instructor notes and lecture slides
Suggested Readings/Materials

Integer Programming. Laurence A. Wolsey, Wiley, 1998. ISBN:  0471283665

Integer and Combinatorial Optimization. Laurence A. Wolsey, George L. Nemhauser, Wiley, 1999. ISBN:  047182819X

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
1
20
Presentation / Jury
Project
Seminar / Workshop
Oral Exams
Midterm
1
40
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
60
Weighting of End-of-Semester Activities on the Final Grade
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
15
4
60
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
1
60
60
Presentation / Jury
0
Project
0
Seminar / Workshop
0
Oral Exam
0
Midterms
1
27
27
Final Exam
1
30
30
    Total
225

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have an appropriate knowledge of methodological and practical elements of the basic sciences and to be able to apply this knowledge in order to describe engineering-related problems in the context of industrial systems.

X
2

To be able to identify, formulate and solve Industrial Engineering-related problems by using state-of-the-art methods, techniques and equipment.

X
3

To be able to use techniques and tools for analyzing and designing industrial systems with a commitment to quality.

X
4

To be able to conduct basic research and write and publish articles in related conferences and journals.

X
5

To be able to carry out tests to measure the performance of industrial systems, analyze and interpret the subsequent results.

X
6

To be able to manage decision-making processes in industrial systems.

X
7

To have an aptitude for life-long learning; to be aware of new and upcoming applications in the field and to be able to learn them whenever necessary.

X
8

To have the scientific and ethical values within the society in the collection, interpretation, dissemination, containment and use of the necessary technologies related to Industrial Engineering.

X
9

To be able to design and implement studies based on theory, experiments and modeling; to be able to analyze and resolve the complex problems that arise in this process; to be able to prepare an original thesis that comply with Industrial Engineering criteria.

X
10

To be able to follow information about Industrial Engineering in a foreign language; to be able to present the process and the results of his/her studies in national and international venues systematically, clearly and in written or oral form.

X

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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