FACULTY OF ENGINEERING

Department of Mechatronics Engineering

CE 485 | Course Introduction and Application Information

Course Name
Linear and Integer Programming
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
CE 485
Fall/Spring
3
0
3
8

Prerequisites
None
Course Language
English
Course Type
Service Course
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course Problem Solving
Lecture / Presentation
Course Coordinator
Course Lecturer(s) -
Assistant(s) -
Course Objectives The primary objective is to develop both an understanding of the formulation techniques, and the algorithms used to solve the class of optimization problems that lend themselves to linear and integer linear programming.
Learning Outcomes The students who succeeded in this course;
  • create LP formulations to appropriate problems.
  • apply simplex and dual simplex methods.
  • express the run-time complexity of various algorithms for solving LP problems.
  • formulate Integer LP (ILP) formulations for various combinatorial problems.
  • employ techniques for relaxation of ILP to LP formulations.
Course Description LP Standard Form, Extreme Points and Basic Solutions, Rudimentary Simplex Algorithm, Interior Point Strategies for LP, Formulating Duals, Primal-to-Dual Relationships, LP-Based Branch and Bound, and Rounding.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Nature of Linear Programs Section 2.4
2 Formulation of Classic LP Model Types Chapter 4
3 LP Standard Form, Extreme Points and Basic Solutions, Rudimentary Simplex Algorithm Section 5.1, Section 5.2, Section 5.3
4 Two Phase Simplex, Degeneracy, Cycling and Finiteness of Simplex Section 5.5, Sections 5.6, Section 5.7
5 Revised Simplex, Lower- and Upper-Bounded Simplex Section 5.8, Section 5.9
6 Interior Point Strategies for LP, Affine Scaling of Solutions, Affine Scaling Search Section 6.1, Section 6.2, Section 6.3
7 Log Barrier Methods for LP, Primal-Dual Search Section 6.4, Section 6.5
8 Midterm
9 Activities vs. Resources, Qualititative Sensitivity Sections 7.1-7.2
10 Quantitative Sensitivity and Duality, Formulating Duals, Primal-to-Dual Relationships Section 7.3, Section 7.4, Section 7.5
11 Solving by Total Enumeration, Elementary Relaxations, Strengthening LP Relaxations Section 12.1, Section 12.2, Section 12.3
12 LP-Based Branch and Bound Section 12.4
13 Rounding, Parent Bounds, Enumeration Sequences and Stopping Early in Branch and Bound Section 12.5
14 Improving Heuristics for Discrete Optimization, Tabu, Simulated Annealing, Genetic Algorithms, Constructive Heuristics for Discrete Optimization Section 12.6, Section 12.7, Section 12.8
15 Review of semester
16 Final Exam

 

Course Notes/Textbooks Optimization in Operations Research, Ronald L. Rardin, Prentice Hall, ISBN-10: 0023984155 • ISBN-13: 9780023984150, 1998.
Suggested Readings/Materials

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Portfolio
Homework / Assignments
Presentation / Jury
Project
1
30
Seminar / Workshop
Oral Exams
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
2
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Theoretical Course Hours
(Including exam week: 16 x total hours)
16
3
48
Laboratory / Application Hours
(Including exam week: '.16.' x total hours)
16
0
Study Hours Out of Class
14
6
84
Field Work
0
Quizzes / Studio Critiques
0
Portfolio
0
Homework / Assignments
0
Presentation / Jury
0
Project
1
60
60
Seminar / Workshop
0
Oral Exam
0
Midterms
1
16
16
Final Exam
1
32
32
    Total
240

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1

To have knowledge in Mathematics, science, physics knowledge based on mathematics; mathematics with multiple variables, differential equations, statistics, optimization and linear algebra; to be able to use theoretical and applied knowledge in complex engineering problems

2

To be able to identify, define, formulate, and solve complex mechatronics engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose.

3

To be able to design a complex electromechanical system, process, device or product with sensor, actuator, control, hardware, and software to meet specific requirements under realistic constraints and conditions; to be able to apply modern design methods for this purpose.

4

To be able to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Mechatronics Engineering applications; to be able to use information technologies effectively.

5

To be able to design, conduct experiments, collect data, analyze and interpret results for investigating Mechatronics Engineering problems.

6

To be able to work effectively in Mechatronics Engineering disciplinary and multidisciplinary teams; to be able to work individually.

7

To be able to communicate effectively in Turkish, both in oral and written forms; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions.

8

To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions.

9

To be aware of ethical behavior, professional and ethical responsibility; information on standards used in engineering applications.

10

To have knowledge about industrial practices such as project management, risk management and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development.

11

Using a foreign language, he collects information about Mechatronics Engineering and communicates with his colleagues. ("European Language Portfolio Global Scale", Level B1)

12

To be able to use the second foreign language at intermediate level.

13

To recognize the need for lifelong learning; to be able to access information; to be able to follow developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechatronics Engineering.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 


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