Course Details

DISCRETE OPTIMIZATION

Course Information

Semester	Course Unit Code	Course Unit Title	T+P+L	Credit	Number of ECTS Credits
1	IE515	DISCRETE OPTIMIZATION	3+0+0	3	7,5

Course Details

Language of Instruction	English
Level of Course Unit	Master's Degree
Department / Program	INDUSTRIAL ENGINEERING
Type of Program	Formal Education
Type of Course Unit	Elective
Course Delivery Method	Face To Face
Objectives of the Course	To provide an understanding of theory, algorithm and applications of combinatorial and integer optimization. To formulate IP models for some real-life decision-making problems and show why one model might be “better” than another equivalent model.
Course Content	This course cover both the theory and the practice of integer programming. Topics include modeling, comparison of alternative formulations, computational complexity, polyhedral theory, valid inequalities, cutting-plane algorithms, enumerative algorithms such as dynamic programming, branch-and-bound, branch-and-cut, heuristic algorithms and techniques to handle large problems such as Benders’ decomposition and delayed column generation (and branch-and-price). Applications include graphs, networks, transportation, and scheduling.
Course Methods and Techniques	We will be using various tools for active learning to take place. This is also a student-driven course. It is your responsibility to participate actively in class discussions.
Prerequisites and co-requisities	None
Course Coordinator	None
Name of Lecturers	Asist Prof.Dr. Rahime Şeyma Bekli seyma.bekli@agu.edu.tr
Assistants	None
Work Placement(s)	No

Recommended or Required Reading

Resources	Wolsey, Laurence A. Integer Programming. Wiley-Interscience, 1998.
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Planned Learning Activities and Teaching Methods

Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria

In-Term Studies	Quantity	Percentage
Yarıl yılSonu Sınavı/Dönem Projesinin Başarı Notuna Katkısı	1	% 20
Ödev	4	% 20
Proje/Çizim	1	% 35
Final examination	1	% 25
Total	7	% 100

ECTS Allocated Based on Student Workload

Activities	Quantity	Duration	Total Work Load
Yazılı Sınav	1	3	3
Sınıf İçi Aktivitesi	14	0	0
Proje	1	50	50
Kişisel Çalışma	14	3	42
Ders dışı çalışma	14	6	84
Yüz Yüze Ders	14	3	42
Final Sınavı	1	3	3
Total Work Load			Number of ECTS Credits 7,5 224

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:

No	Learning Outcomes
1	Learn how integer variables are used in constructing complex mathematical models.
2	Grasp the fundamental concepts of polyhedral theory and their relevance to integer programming.
3	Gain the ability to evaluate the complexity of integer programming problems using tools from complexity theory.
4	Apply exact solution methods to solve integer programming models.
5	Construct decomposition methods for large size problems.
6	Design a team project to solve a real-world problem with integer and combinatorial optimization and share the results of a real-world problem related team project (written and orally) with peers in a meaningful and professional manner.

Weekly Detailed Course Contents

Week	Topics	Study Materials	Materials
1	Formulations and comparisons
2	Methods of strengthening formulations
3	Computational complexity for algorithms
4	Computational complexity for problem classes, P and NP classes
5	Simplex algorithm
6	Easily solvable problems, total unimodality
7	Dynamic programming
8	Fall break
9	Lecture Free Week Project Progress Presentations
10	Polyhedron theory, valid inequalities and strengthening of them
11	Structured Inequalities and Lifting
12	Cutting plane algorithms, Separation Problem, branch and cut
13	Column Generation and Pricing Problem
14	Benders decomposition

Contribution of Learning Outcomes to Programme Outcomes

Contribution: 1: Very Slight 2:Slight 3:Moderate 4:Significant 5:Very Significant

https://sis.agu.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=77276&lang=en