Linear Optimization (MDES655) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Linear Optimization MDES655 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English
Course Type N/A
Course Level Natural & Applied Sciences Master's Degree
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 -


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 X
Major Area Courses
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 Ability to expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement.
2 Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering.
3 To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines.
4 Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed.
5 Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions.
6 Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs.
7 Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process.
8 Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility.
9 To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level.
10 Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments.
11 To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications.
12 Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 3 48
Special Course Internship 1 20 20
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
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