STOCHASTIC MODELS

AIM

This course aims to introduce basic stochastic models in order to deal with uncertainties in Industrial engineering problems and presents how to develop Markov models to reflect stochastic processes faced in real life situations.

CONTENT

This course contains; Introduction to the Course,Review of Probability Theory,Conditional Probability and Conditional Expectation,Introduction to Stochastic Processes and Markov Chains,Discrete Time Markov Chains-1,Discrete Time Markov Chains-2,The Exponential Distribution and Poisson Process-1,The Exponential Distribution and Poisson Process-2,Continuous Time Markov Chains-1,Continuous Time Markov Chains-2,Queuing Systems-1,Queuing Systems-2,Queuing Systems-3,General Review.

1. 1

   1. Students differentiate deterministic and stochastic systems and apply fundamental concepts of probability theory to analyze uncertainty.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

2. 2

   2. Students implement modeling methodologies of uncertainty in industrial engineering problems.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

3. 3

   3. Students define the exponential distribution and its relationship with the Poisson process.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

4. 4

   4. Students analyze Markov Chain models.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

5. 5

   5. Students defıne queuing theory.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

6. 6

   6. The student analyzes industrial engineering problems holistically using stochastic modeling methods, develops appropriate solution approaches, and interprets the results.

   Taught by: Question - Answer Technique, Experiential Learning, Lecture Method · Assessed by: Traditional Written Exam, Homework

WEEKLY PLAN

1. WEEK 1

   Introduction to the Course

2. WEEK 2

   Review of Probability Theory

3. WEEK 3

   Conditional Probability and Conditional Expectation

4. WEEK 4

   Introduction to Stochastic Processes and Markov Chains

5. WEEK 5

   Discrete Time Markov Chains-1

6. WEEK 6

   Discrete Time Markov Chains-2

7. WEEK 7

   The Exponential Distribution and Poisson Process-1

8. WEEK 8

   The Exponential Distribution and Poisson Process-2

9. WEEK 9

   Continuous Time Markov Chains-1

10. WEEK 10

    Continuous Time Markov Chains-2

11. WEEK 11

    Queuing Systems-1

12. WEEK 12

    Queuing Systems-2

13. WEEK 13

    Queuing Systems-3

14. WEEK 14

    General Review

ASSESSMENT

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

WORKLOAD

READING

• Introduction to Probability Models by Sheldon Ross, Academic Press. Operations Research: Applications & Algorithms by W.L. Winston Thomson
• Operations Research: Applications & Algorithms by W.L. Winston Thomson, ISBN: 0-534-42362-0.

TEACHING STAFF

• Assist.Prof. Engin SANSARCICOORDINATOR
• Assist.Prof. Engin SANSARCI