INTRODUCTION to MODELLING and OPTIMIZATION

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).

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.

1. 1

   Students define modeling concepts.

   Taught by: Problem Solving Method, Case Study Method, Self Study Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework, Quiz, Performance Task

2. 2

   Students analyze mathematical models.

   Taught by: Problem Solving Method, Case Study Method, Self Study Method, Question - Answer Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework, Performance Task

3. 3

   Students formulate problems using linear programming.

   Taught by: Problem Solving Method, Self Study Method, Question - Answer Technique, Simulation Technique, Experiential Learning, Flipped Classroom Learning, Lecture Method · Assessed by: Traditional Written Exam, Quiz

4. 4

   Students implement the Simplex algorithm.

   Taught by: Problem Solving Method, Self Study Method, Question - Answer Technique, Flipped Classroom Learning, Lecture Method · Assessed by: Quiz

5. 5

   Students define duality and sensitivity analysis.

   Taught by: Problem Solving Method, Self Study Method, Question - Answer Technique, Lecture Method · Assessed by: Traditional Written Exam

6. 6

   Students solve transportation and assignment models.

   Taught by: Problem Solving Method, Self Study Method, Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam

WEEKLY PLAN

1. WEEK 1

   Introduction to Model Building

   Preparation: Examining the course textbook

2. WEEK 2

   Basic Linear Algebra

   Preparation: Examining the course textbook

3. WEEK 3

   Introduction to Linear Programming

   Preparation: Examining the course textbook

4. WEEK 4

   Convex Sets and Functions, Extreme Points and Optimality, Graphical Solution

   Preparation: Examining the course textbook

5. WEEK 5

   Graphical Sensitivity Analysis and Computer Based Solutions

   Preparation: Examining the course textbook

6. WEEK 6

   Simplex Algorithm

   Preparation: Examining the course textbook

7. WEEK 7

   Simplex Algorithm: Artificial Starting Solutions

   Preparation: Examining the course textbook

8. WEEK 8

   Simplex Algorithm: Artificial Starting Solutions and Special Cases in Simplex

   Preparation: Examining the course textbook

9. WEEK 9

   Revised Simplex

   Preparation: Examining the course textbook

10. WEEK 10

    Special Simplex Implementations: Karus-Kuhn-Tucker Optimality Conditions

    Preparation: Examining the course textbook

11. WEEK 11

    Duality and Sensitivity

    Preparation: Examining the course textbook

12. WEEK 12

    Duality and Sensitivity: Dual Simplex

    Preparation: Examining the course textbook

13. WEEK 13

    Transportation and Assignment Problems-1

    Preparation: Examining the course textbook

14. WEEK 14

    Transportation and Assignment Problems-2

    Preparation: Examining the course textbook

ASSESSMENT

• Rate of Midterm Exam to Success30%
• Rate of Final Exam to Success70%

WORKLOAD

READING

• 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)

TEACHING STAFF

• Lect.Dr. Esin TETİKCOORDINATOR
• Assoc.Prof. Yasin GÖÇGÜN