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
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
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
X
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
X
6
6. An ability to function on multidisciplinary teams
X
7
7. An ability to communicate effectively
X
8
8. A recognition of the need for, and an ability to engage in life-long learning
X
9
9. An understanding of professional and ethical responsibility
X
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
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.
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
1. An ability to apply knowledge of mathematics, science, and engineering
X
2
2. An ability to identify, formulate, and solve engineering problems
X
3
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
X
4
4. An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
X
5
5. An ability to design and conduct experiments, as well as to analyze and interpret data
X
6
6. An ability to function on multidisciplinary teams
X
7
7. An ability to communicate effectively
X
8
8. A recognition of the need for, and an ability to engage in life-long learning
X
9
9. An understanding of professional and ethical responsibility
X
10
10. A knowledge of contemporary issues
11
11. The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
