The aim and objective of this course are to teach. how to formulate and analyze mathematical models (with selected real-world applications)and, mathematical tools to handle linear programming and network problems (the simplex method, duality, sensitivity analysis, and related topics, network models, and project scheduling).
Course Content
This course contains; Introduction to Model Building,Basic Linear Algebra,Introduction to Linear Programming,Convex Sets and Functions, Extreme Points and Optimality, Graphical Solution,Graphical Sensitivity Analysis and Computer Based Solutions,Simplex Algorithm
,Simplex Algorithm: Artificial Starting Solutions,Simplex Algorithm: Artificial Starting Solutions and Special Cases in Simplex,Revised Simplex ,Special Simplex Implementations: Karus-Kuhn-Tucker Optimality Conditions,Duality and Sensitivity,Duality and Sensitivity: Dual Simplex,Transportation and Assignment Problems-1,Transportation and Assignment Problems-2.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
Students define modeling concepts.
12, 13, 14, 16, 6, 8, 9
A, E, G, H
Students analyze mathematical models.
12, 13, 14, 16, 6, 8, 9
A, E, H
Students formulate problems using linear programming.
12, 14, 16, 21, 6, 8, 9
A, G
Students implement the Simplex algorithm.
12, 14, 16, 8, 9
G
Students define duality and sensitivity analysis.
12, 14, 16, 9
A
Students solve transportation and assignment models.
12, 14, 16, 6, 9
A
Teaching Methods:
12: Problem Solving Method, 13: Case Study Method, 14: Self Study Method, 16: Question - Answer Technique, 21: Simulation Technique, 6: Experiential Learning, 8: Flipped Classroom Learning, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam, E: Homework, G: Quiz, H: Performance Task
Course Outline
Order
Subjects
Preliminary Work
1
Introduction to Model Building
Examining the course textbook
2
Basic Linear Algebra
Examining the course textbook
3
Introduction to Linear Programming
Examining the course textbook
4
Convex Sets and Functions, Extreme Points and Optimality, Graphical Solution
Examining the course textbook
5
Graphical Sensitivity Analysis and Computer Based Solutions
Examining the course textbook
6
Simplex Algorithm
Examining the course textbook
7
Simplex Algorithm: Artificial Starting Solutions
Examining the course textbook
8
Simplex Algorithm: Artificial Starting Solutions and Special Cases in Simplex
Examining the course textbook
9
Revised Simplex
Examining the course textbook
10
Special Simplex Implementations: Karus-Kuhn-Tucker Optimality Conditions
Examining the course textbook
11
Duality and Sensitivity
Examining the course textbook
12
Duality and Sensitivity: Dual Simplex
Examining the course textbook
13
Transportation and Assignment Problems-1
Examining the course textbook
14
Transportation and Assignment Problems-2
Examining the course textbook
Resources
Taha, Hamdy A., Operations Research, 8th edition, 2007. ISBN: 0131360140
Winston, Wayne L., Operations Research: Applications and Algorithms, 4th edition, 2003. ISBN-13: 978-0534380588 (Course notes and other material may be provided by the instructor)
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering.
X
2
An ability to identify, formulate, and solve engineering problems.
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability.
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
5
An ability to design and conduct experiments, as well as to analyze and interpret data.
6
An ability to function on multidisciplinary teams.
X
7
An ability to communicate effectively.
X
8
A recognition of the need for, and an ability to engage in life-long learning.
X
9
An understanding of professional and ethical responsibility.
X
10
A knowledge of contemporary issues.
X
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.
X
Assessment Methods
Contribution Level
Absolute Evaluation
Rate of Midterm Exam to Success
30
Rate of Final Exam to Success
70
Total
100
ECTS / Workload Table
Activities
Number of
Duration(Hour)
Total Workload(Hour)
Course Hours
14
3
42
Guided Problem Solving
14
2
28
Resolution of Homework Problems and Submission as a Report
14
2
28
Term Project
0
0
0
Presentation of Project / Seminar
0
0
0
Quiz
4
15
60
Midterm Exam
1
30
30
General Exam
1
40
40
Performance Task, Maintenance Plan
0
0
0
Total Workload(Hour)
228
Dersin AKTS Kredisi = Toplam İş Yükü (Saat)/30*=(228/30)
8
ECTS of the course: 30 hours of work is counted as 1 ECTS credit.
Detail Informations of the Course
Course Description
Course
Code
Semester
T+P (Hour)
Credit
ECTS
INTRODUCTION to MODELLING and OPTIMIZATION
CEE3249050
Spring Semester
3+2
4
8
Course Program
Perşembe 13:30-14:15
Perşembe 14:30-15:15
Perşembe 15:30-16:15
Cumartesi 11:00-11:45
Cumartesi 12:00-12:45
Prerequisites Courses
Recommended Elective Courses
Language of Course
English
Course Level
First Cycle (Bachelor's Degree)
Course Type
Elective
Course Coordinator
Assoc.Prof. Yasin GÖÇGÜN
Name of Lecturer(s)
Assoc.Prof. Yasin GÖÇGÜN
Assistant(s)
Aim
The aim and objective of this course are to teach. how to formulate and analyze mathematical models (with selected real-world applications)and, mathematical tools to handle linear programming and network problems (the simplex method, duality, sensitivity analysis, and related topics, network models, and project scheduling).
Course Content
This course contains; Introduction to Model Building,Basic Linear Algebra,Introduction to Linear Programming,Convex Sets and Functions, Extreme Points and Optimality, Graphical Solution,Graphical Sensitivity Analysis and Computer Based Solutions,Simplex Algorithm
,Simplex Algorithm: Artificial Starting Solutions,Simplex Algorithm: Artificial Starting Solutions and Special Cases in Simplex,Revised Simplex ,Special Simplex Implementations: Karus-Kuhn-Tucker Optimality Conditions,Duality and Sensitivity,Duality and Sensitivity: Dual Simplex,Transportation and Assignment Problems-1,Transportation and Assignment Problems-2.
Dersin Öğrenme Kazanımları
Teaching Methods
Assessment Methods
Students define modeling concepts.
12, 13, 14, 16, 6, 8, 9
A, E, G, H
Students analyze mathematical models.
12, 13, 14, 16, 6, 8, 9
A, E, H
Students formulate problems using linear programming.
12, 14, 16, 21, 6, 8, 9
A, G
Students implement the Simplex algorithm.
12, 14, 16, 8, 9
G
Students define duality and sensitivity analysis.
12, 14, 16, 9
A
Students solve transportation and assignment models.
12, 14, 16, 6, 9
A
Teaching Methods:
12: Problem Solving Method, 13: Case Study Method, 14: Self Study Method, 16: Question - Answer Technique, 21: Simulation Technique, 6: Experiential Learning, 8: Flipped Classroom Learning, 9: Lecture Method
Assessment Methods:
A: Traditional Written Exam, E: Homework, G: Quiz, H: Performance Task
Course Outline
Order
Subjects
Preliminary Work
1
Introduction to Model Building
Examining the course textbook
2
Basic Linear Algebra
Examining the course textbook
3
Introduction to Linear Programming
Examining the course textbook
4
Convex Sets and Functions, Extreme Points and Optimality, Graphical Solution
Examining the course textbook
5
Graphical Sensitivity Analysis and Computer Based Solutions
Examining the course textbook
6
Simplex Algorithm
Examining the course textbook
7
Simplex Algorithm: Artificial Starting Solutions
Examining the course textbook
8
Simplex Algorithm: Artificial Starting Solutions and Special Cases in Simplex
Examining the course textbook
9
Revised Simplex
Examining the course textbook
10
Special Simplex Implementations: Karus-Kuhn-Tucker Optimality Conditions
Examining the course textbook
11
Duality and Sensitivity
Examining the course textbook
12
Duality and Sensitivity: Dual Simplex
Examining the course textbook
13
Transportation and Assignment Problems-1
Examining the course textbook
14
Transportation and Assignment Problems-2
Examining the course textbook
Resources
Taha, Hamdy A., Operations Research, 8th edition, 2007. ISBN: 0131360140
Winston, Wayne L., Operations Research: Applications and Algorithms, 4th edition, 2003. ISBN-13: 978-0534380588 (Course notes and other material may be provided by the instructor)
Course Contribution to Program Qualifications
Course Contribution to Program Qualifications
No
Program Qualification
Contribution Level
1
2
3
4
5
1
An ability to apply knowledge of mathematics, science, and engineering.
X
2
An ability to identify, formulate, and solve engineering problems.
X
3
An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability.
4
An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice.
5
An ability to design and conduct experiments, as well as to analyze and interpret data.
6
An ability to function on multidisciplinary teams.
X
7
An ability to communicate effectively.
X
8
A recognition of the need for, and an ability to engage in life-long learning.
X
9
An understanding of professional and ethical responsibility.
X
10
A knowledge of contemporary issues.
X
11
The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context.