Department of Industrial Engineering

IE 357 | Course Introduction and Application Information

Course Name

Special Topics in Optimization

Code	Semester	Theory (hour/week)	Application/Lab (hour/week)	Local Credits	ECTS
IE 357	FALL	3	0	3	6

Prerequisites	IE 252 To be successful (To have received at least DD grade)
Course Language	English
Course Type	ELECTIVE_COURSE
Course Level	First Cycle
Mode of Delivery	Face-To-Face
Teaching Methods and Techniques of the Course	Lecture / Presentation
National Occupational Classification Code	-
Course Coordinator	Prof. Dr. Selin Özpeynirci
Course Lecturer(s)	Prof. Dr. Selin Özpeynirci
Assistant(s)	-

Course Objectives

This course aims to teach advanced solution techniques and algorithms for large-scale integer programming problems. It covers methods such as linear programming relaxations, Dantzig-Wolfe decomposition, branch-and-bound algorithm, Lagrangian relaxation, cutting plane methods, Benders decomposition, and dynamic programming. The course seeks to provide students with a comprehensive understanding of the theoretical foundations and practical applications of these techniques.

Learning Outcomes

The students who succeeded in this course;

Name	Description	PC Sub	* Contribution Level
Name	Description	PC Sub	1	2	3	4	5
LO1	Students will be able to identify the limitations of classical optimization techniques.	1.5			X
LO2	Students will be able to explain the principles of linear programming relaxation.	4				X
LO3	Students will be able to apply methods such as Dantzig-Wolfe decomposition, branch-and-bound algorithm, and Lagrangian relaxation to large-scale integer programming problems, along with their justifications.	4				X
LO4	Students will be able to adapt Benders decomposition and dynamic programming techniques to solve various optimization problems encountered in practice.	4				X

Course Description

Classical Optimization Methods, Linear Programming Relaxation, Dantzig-Wolfe Decomposition, Branch-and-Bound Algorithm, Lagrangian Relaxation, Cutting Plane Method, Benders Decomposition

Related Sustainable Development Goals

Course Category	Core Courses
	Major Area Courses	X
	Supportive Courses
	Media and Managment Skills Courses
	Transferable Skill Courses

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week	Subjects	Required Materials	Learning Outcome
1	Review of Optimization Fundamentals	Lecture Notes	LO1
2	Solution Methods for Large-Scale Integer Programming Problems: Linear Programming Relaxations	Lecture Notes	LO2
3	Solution Methods for Large-Scale Integer Programming Problems: Dantzig&Wolfe Algorithm	Lecture Notes	LO3
4	Solution Methods for Large-Scale Integer Programming Problems: Branch and Bound Algorithm	Lecture Notes	LO3
5	Solution Methods for Large-Scale Integer Programming Problems: Branch and Bound Algorithm	Lecture Notes	LO3
6	Solution Methods for Large-Scale Integer Programming Problems: Lagrangian Relaxation	Lecture Notes	LO3
7	Solution Methods for Large-Scale Integer Programming Problems: Lagrangian Relaxation	Lecture Notes	LO3
8	Midterm Exam		-
9	Solution Methods for Large-Scale Integer Programming Problems: Branch and Cut Algorithm	Lecture Notes	LO3
10	Solution Methods for Large-Scale Integer Programming Problems: Cutting Plane Algorithm	Lecture Notes	LO3
11	Solution Methods for Large-Scale Integer Programming Problems: Benders Decomposition	Lecture Notes	LO4
12	Midterm		-
13	Dynamic Programming	Lecture Notes	LO4
14	Dynamic Programming	Lecture Notes	LO4
15	Review		-
16	Final Exam		-

Course Notes/Textbooks	Wolsey L. A. and Nemhauser G. L. (2014). Integer and combinatorial optimization. John Wiley and Sons.
Suggested Readings/Materials	Martin R. K. (2012) Large scale linear and integer optimization a unified approach. Springer Science and Business Media.

EVALUATION SYSTEM

Semester Activities	Number	Weighting	LO1	LO2	LO3	LO4
Midterm	2	60	X	X	X	X
Final Exam	1	40	X	X	X	X
Total	3	100

ECTS / WORKLOAD TABLE

Semester Activities	Number	Duration (Hours)	Workload
Participation	-	-	-
Theoretical Course Hours	16	3	48
Laboratory / Application Hours	14	4	56
Study Hours Out of Class	-	-	-
Field Work	-	-	-
Quizzes / Studio Critiques	-	-	-
Portfolio	-	-	-
Homework / Assignments	-	-	-
Presentation / Jury	-	-	-
Project	-	-	-
Seminar / Workshop	-	-	-
Oral Exams	-	-	-
Midterms	2	22	44
Final Exam	1	32	32
		Total	180

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#	PC Sub	Program Competencies/Outcomes	* Contribution Level
#	PC Sub	Program Competencies/Outcomes	1	2	3	4	5
1	Engineering Knowledge: Knowledge of mathematics, science, basic engineering, computation, and related engineering discipline-specific topics; the ability to apply this knowledge to solve complex engineering problems.
	1	Mathematics
	2	Science
	3	Basic Engineering
	4	Computation
	5	Related engineering discipline-specific topics			LO1
	6	The ability to apply this knowledge to solve complex engineering problems
2	Problem Analysis: Ability to identify, formulate and analyze complex engineering problems using basic knowledge of science, mathematics and engineering, and considering the UN Sustainable Development Goals relevant to the problem being addressed.
3	Engineering Design: The ability to devise creative solutions to complex engineering problems; the ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions.
	1	Ability to design creative solutions to complex engineering problems
	2	Ability to design complex systems, processes, devices or products to meet current and future needs, considering realistic constraints and conditions
4	Use of Techniques and Tools: Ability to select and use appropriate techniques, resources, and modern engineering and computing tools, including estimation and modeling, for the analysis and solution of complex engineering problems, while recognizing their limitations.					LO2 LO3 LO4
5	Research and Investigation: Ability to use research methods to investigate complex engineering problems, including literature research, designing and conducting experiments, collecting data, and analyzing and interpreting results.
	1	Literature research for the study of complex engineering problems
	2	Designing experiments
	3	Ability to use research methods, including conducting experiments, collecting data. analyzing and interpreting results
6	Global Impact of Engineering Practices: Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals; awareness of the legal implications of engineering solutions.
	1	Knowledge of the impacts of engineering practices on society, health and safety, economy, sustainability, and the environment, within the context of the UN Sustainable Development Goals
	2	Awareness of the legal implications of engineering solutions
7	Ethical Behavior: Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility; awareness of being impartial, without discrimination, and being inclusive of diversity.
	1	Acting in accordance with the principles of the engineering profession, knowledge about ethical responsibility ethical responsibility
	2	Awareness of being impartial and inclusive of diversity, without discriminating on any subject
8	Individual and Teamwork: Ability to work effectively, individually and as a team member or leader on interdisciplinary and multidisciplinary teams (face-to-face, remote or hybrid).
	1	Ability to work individually and within the discipline
	2	Ability to work effectively as a team member or leader in multidisciplinary teams (face-to-face, remote or hybrid)
9	Verbal and Written Communication: Taking into account the various differences of the target audience (such as education, language, profession) on technical issues.
	1	Ability to communicate verbally
	2	Ability to communicate effectively in writing
10	Project Management: Knowledge of business practices such as project management and economic feasibility analysis; awareness of entrepreneurship and innovation.
	1	Knowledge of business practices such as project management and economic feasibility analysis
	2	Awareness of entrepreneurship and innovation
11	Lifelong Learning: Lifelong learning skills that include being able to learn independently and continuously, adapting to new and developing technologies, and thinking questioningly about technological changes.