ADVANCED MODELING 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; Model Building,Advanced Linear Programming,Convex Sets and Functions, Extreme Points and Optimality,,Simplex Algorithm,Revised simplex, Karush-Kuhn-Tucker Optimality Conditions,Duality and Sensitivity: Dual Simplex,Approximation and fitting ,Geometric problems,Geometric problems 2,Unconstrained minimization ,Unconstrained minimization 2,Equality constrained minimization,Interior-point methods,Interior-point methods 2 .

1. 1

   Defines 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

   Understands the concept of mathematical models and analyzing 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

   Formulates problems through linear programming and solves them using the necessary techniques.

   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

   Understands the Simplex algorithm and the solution with the Simplex algorithm (initial solution, convergence, two-phase-large M methods, revised simplex, etc.).

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

5. 5

   Understands duality and sensitivity analysis.

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

6. 6

   Understands transportation and assignment models.

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

7. 7

   Solves 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

   Model Building

   Preparation: Lecture Notes

2. WEEK 2

   Advanced Linear Programming

   Preparation: Lecture Notes

3. WEEK 3

   Convex Sets and Functions, Extreme Points and Optimality,

   Preparation: Lecture Notes

4. WEEK 4

   Simplex Algorithm

   Preparation: Lecture Notes

5. WEEK 5

   Revised simplex, Karush-Kuhn-Tucker Optimality Conditions

   Preparation: Lecture Notes

6. WEEK 6

   Duality and Sensitivity: Dual Simplex

   Preparation: Lecture Notes

7. WEEK 7

   Approximation and fitting

   Preparation: Lecture Notes

8. WEEK 8

   Geometric problems

   Preparation: Lecture Notes

9. WEEK 9

   Geometric problems 2

   Preparation: Lecture Notes

10. WEEK 10

    Unconstrained minimization

    Preparation: Lecture Notes

11. WEEK 11

    Unconstrained minimization 2

    Preparation: Lecture Notes

12. WEEK 12

    Equality constrained minimization

    Preparation: Lecture Notes

13. WEEK 13

    Interior-point methods

    Preparation: Lecture Notes

14. WEEK 14

    Interior-point methods 2

    Preparation: Lecture Notes

ASSESSMENT

• Rate of Midterm Exam to Success50%
• Rate of Final Exam to Success50%

WORKLOAD

READING

• 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)
• Convex Optimization; S. Boyd, L.Vandenberghe, Cambridge university press, 2004

TEACHING STAFF

• Assoc.Prof. Yasin GÖÇGÜNCOORDINATOR
• Assoc.Prof. Yasin GÖÇGÜN