Linear Optimization (MDES655) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Linear Optimization MDES655 Elective Courses 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language İngilizce
Course Type Elective Courses Taken From Other Departments
Course Level Doktora
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives This course aims to give to Ph.D. students from different engineering backgrounds the skills of real life problem formulation with linear optimization along with the use of basic computer packages to solve the problems.
Course Learning Outcomes The students who succeeded in this course;
  • 1. Students will have a vision of linear optimization and duality. 2. Students will get a perspective of linear optimization algorithms and be able to code and implement algorithms. 3. Students will develop a vision of the application areas of linear optimization. 4. Students will have a knowledge of decomposition techniques especially for large scaled linear optimization problems. 5. Students will be familiarized with algorithmic complexity and convergence issues.
Course Content Sets of linear equations, linear feasibility and optimization, local and global optima, the Simplex method and its variants, theory of duality and the dual-Simplex method, network-Simplex algorithms, computational complexity issues and interior-point algorithms.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 An introduction to linear feasibility and linear optimization problems. Related pages of the textbook and other courses
2 Geometry of linear optimization, polyhedral sets, extreme points and basic feasible solutions. Related pages of the textbook and other courses
3 The Simplex Algorithm. Related pages of the textbook and other courses
4 Duality theory and complementary slackness. Related pages of the textbook and other courses
5 Sensitivity analysis and parametric linear programming. Related pages of the textbook and other courses
6 The Dual Simplex Algorithm. Related pages of the textbook and other courses
7 Extensions of the Simplex Method. Simplex with upper and lower bounds. Related pages of the textbook and other courses
8 Midterm -
9 Algorithms with sparse matrices and decomposition techniques. Related pages of the textbook and other courses
10 The network-flow problems and the Network Simplex Method. Related pages of the textbook and other courses
11 Application issues of linear optimization. Related pages of the textbook and other courses
12 Algorithmic complexity of the Simplex Method. Related pages of the textbook and other courses
13 The ellipsoid method and an overview of interior-point algorithms. Related pages of the textbook and other courses
14 Algorithm coding and presentations. Related pages of the textbook and other courses
15 Overall review -
16 Final exam -

Sources

Course Book 1. [1] S.G. Nash and A. Sofer, Linear and Nonlinear Programming, McGraw Hill 1996.
Other Sources 2. [2] V. Chvatal, Linear Programming, Freeman 1983.
3. [3] G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, Wiley 1988.
4. [4] H.P. Williams, Model Building in Mathematical Programming, 2nd edition, Wiley, 1985.
5. [5] F.S. Hillier and G.J. Lieberman, Introduction to Mathematical Programming, 2nd edition, McGraw-Hill, 1995.

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work 1 15
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 3 25
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 30
Toplam 6 100
Percentage of Semester Work 70
Percentage of Final Work 30
Total 100

Course Category

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

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Gains the ability to understand and apply knowledge in the fields of mathematics, science and basic sciences at the level of expertise.
2 Gains the ability to access wide and deep knowledge in the field of Engineering by doing scientific research with current techniques and methods, evaluate, interpret and implement the gained knowledge.
3 Being aware of the latest developments his/her field of study, defines problems, formulates and develops new and/or original ideas and methods in solutions.
4 Designs and applies theoretical, experimental, and model-based research, analyzes and interprets the results obtained at the level of expertise.
5 Gains the ability to use the applications, techniques, modern tools and equipment in his/her field of study at the level of expertise.
6 Designs, executes and finalizes an original work process independently.
7 Can work in interdisciplinary and interdisciplinary teams, lead teams, use the information of different disciplines together and develop solution approaches.
8 Pays regard to scientific, social and ethical values in all professional activities and acquires responsibility consciousness at the level of expertise.
9 Contributes to the literature by communicating the processes and results of his/her academic studies in written form or orally in national and international academic environments, communicates effectively with communities and scientific staff working in the field of specialization.
10 Gains the skill of lifelong learning at the level of expertise.
11 Communicates verbally and in written form using a foreign language at least at the European Language Portfolio B2 General Level.
12 Recognizes the social, environmental, health, safety, legal aspects of engineering applications, as well as project management and business life practices, being aware of the limitations they place on engineering applications.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Laboratory
Application
Special Course Internship 1 20 20
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments 3 6 18
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 8 8
Prepration of Final Exams/Final Jury 1 10 10
Total Workload 136