Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
7ENM409Graf-Çizge Teorisi3+0+03530.10.2026
Course Details
Language of Instruction Turkish
Level of Course Unit Bachelor'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 The course aims to present the methods and techniques used to solve mathematical models that facilitate optimal decision-making and to introduce their real-world applications. It seeks to define basic solution approaches for linear programming problems while providing detailed information on solution methods for transportation problems. Through illustrative examples of assignment problems, the course aims to equip students with the skills to perform network analysis, which constitutes a significant portion of the curriculum. Each lecture will conclude with practical examples to reinforce the material presented. Ultimately, by establishing the necessary theoretical foundation at the undergraduate level, the course aims to enable graduates to model and analyze problems encountered in the public and private sectors and to acquire the knowledge and skills required to interpret analysis results.
Course Content CHAPTER 1: Introduction to Linear Programming
CHAPTER 2: Simplex Algorithm
CHAPTER 3: Sensitivity Analysis
CHAPTER 4: Primal-Dual Relationship
CHAPTER 5: Integer Programming
CHAPTER 6: Dual Simplex Method
Course Methods and Techniques onsite
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Asist Prof.Dr. Metehan ATAY metehan.atay@hku.edu.tr
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources Operations Research: An Introduction, Hamdy Taha, Ninth Ed., Pearson, 2011. 2- Introduction to Operations Research, Frederich S. Hillier, Gerald J. Lieberman, Ninth Ed. McGraw-Hill, 2010
Course Notes 1- Operations Research: An Introduction, Hamdy Taha, Ninth Ed., Pearson, 2011.
2- Introduction to Operations Research, Frederich S. Hillier, Gerald J. Lieberman, Ninth Ed. McGraw-Hill, 2010
Documents .
Assignments .
Exams .

Course Category
Field %100

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
Mid-terms 1 % 40
Final examination 1 % 60
Total
2
% 100

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 15 4 60
Hours for off-the-c.r.stud 15 4 60
Presentation 12 2 24
Mid-terms 1 3 3
Final examination 1 3 3
Total Work Load   Number of ECTS Credits 5 150

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
Beceri 
2 Hesaplamalı karmaşıklık teorisinden yola çıkarak kurduğu modelin çözüm süresi ve etkinliğini hesaplayabilme becerisi.
4 Doğrusal olarak programlanmış modellerin tam sayılı çözümlerine ulaşmaya ilişkin metotları kullanabilme becerisi.
Yetkinlik 
1 1. Ulaştırma ve Ağ modellerine anlayabilme , Modelleye bilme ve Çözüme ulaştırmak için farklı metotlar kullanabilme yeteneği.
3 Farklı problem türlerine dair uygun algoritmaları kullanabilme ve optimizasyon uzmanlığı.
5 Doğrusal olmayan matematiksel modelleri modelleyebilme ve çözümleyebilme yeteneği.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Overview: Operations Research as a scientific field, Linear Programming (LP), and model examples.
2 Different forms of D/P problems and their equivalence; basic concepts and properties of solutions
3 Optimality Criterion; Simplex algorithm for a D/P problem with an identifiable basic solution.
4 Artificial basic solution method
5 Dual D/P problems; Primal-Dual relationships; Primal-Dual calculations
6 Dual D/P problems; Primal-Dual relationships; Primal-Dual calculations (continued).
7 Dual Simplex method
8 .
9 Economic interpretation of duality
10 Transportation Models: Definition and initial solution techniques
11 Transportation Models: Optimum Solution Techniques
12 Assignment Model
13 .
14 .
15 .

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14 P15 P16 P17 P18 P19 P20 P21 P22 P23 P24
All 5
Sk2 5 5 5 5 3 3
Sk4 5 5 5 5 3 3
Co1 5 5 5 5 3 3
Co3 5 5 5 5 3 3
Co5 5 5 5 5 3 3

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