Introduction To Stochastic Processes(IND405)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| IND405 | Introduction To Stochastic Processes | 7 | 3 | 0 | 0 | 3 | 4 |
| Prerequisites | IND211 |
| Admission Requirements | IND211 |
| Language of Instruction | English |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | EBRU ANGÜN ebru.angun@gmail.com (Email) |
| Assistant | |
| Objective |
The stochastic processes enable students to model and analyze systems with random components. These stochastic models have several application areas such as supply chain management, inventory systems management, and call-center management. This course aims at introducing different types of stochastic models and their analyses, which can further be useful for students in their graduate studies and in industry. Consequently, the objectives of this course are as follows: 1- Enable students to model a given problem through different types of stochastic models 2- Enable students to analyze stochastic models 3- Enable students to apply their knowledge of stochastic processes to queueing and inventory models |
| Content |
Review of probability (Ross, Chapter 1) Conditional probability and conditional expectation (Ross, Chapter 3) Markov chains, Chapman-Kolmogorov equations, and classification of states (Ross, Chapter 4) Gambler’s ruin problem, branching process (Ross, Chapter 4) Poisson processes and exponential distribution (Ross, Chapter 5) Markov processes, birth and death processes (Ross, Chapter 6) Birth and death processes, transition and limiting probabilities (Ross, Chapter 6) Queueing models (Ross, Chapter 8) Inventory models (Ross, Chapter 9) |
| Course Learning Outcomes |
Upon successful completion of this course, the student will be able to LO 1: Define different types of stochastic models. LO 2: Build an appropriate stochastic model for a given problem. LO 3: Analyze the performance criteria of a stochastic model. LO 4: Build an appropriate stochastic model for queueing and inventory problems. LO 5: Analyze the performance criteria of queueing and inventory systems. |
| Teaching and Learning Methods |
Explain the subjects in class Encourage students to discuss Show how to build stochastic models in class through exercises |
| References | Ross, S., “Introduction to Probability Models”, 9th Edition, Academic Press, New York, 2007. |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Review of probability (Ross, Chapter 1) |
| 2 | Conditional probability (Ross, Chapter 3) |
| 3 | Conditional expectation (Ross, Chapter 3) |
| 4 | Markov chains, Chapman-Kolmogorov equations, and classification of states (Ross, Chapter 4) |
| 5 | Markov chains, Chapman-Kolmogorov equations, and classification of states (Ross, Chapter 4) |
| 6 | Gambler’s ruin problem, branching process (Ross, Chapter 4) |
| 7 | Poisson process and exponential distribution (Ross, Chapter 5) |
| 8 | Poisson process and exponential distribution (Ross, Chapter 5) |
| 9 | Midterm |
| 10 | Markov process, birth and death processes (Ross, Chapter 6) |
| 11 | Markov process, birth and death processes (Ross, Chapter 6) Birth and death processes, transition and limiting probabilities (Ross, Chapter 6) |
| 12 | Queueing and inventory models |
| 13 | Queueing and inventory models |
| 14 | Midterm |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 60 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 2 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering | X | ||||
| 2 | Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions | X | ||||
| 3 | Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering | X | ||||
| 4 | Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design | |||||
| 5 | Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology | X | ||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | |||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | |||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | |||||
| 9 | Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management | |||||
| 10 | Awareness of professional and ethical responsibility | |||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | |||||
| 12 | Knowledge on entrepreneurship, innovation and sustainability | |||||
| 13 | Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety. | |||||
| 14 | Knowledge of the problems of contemporary society | |||||
| 15 | Knowledge of the legal implications of the practice of industrial engineering | |||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Working Hours out of Class | 13 | 2 | 26 |
| Assignments | 0 | 0 | 0 |
| Presentation | 0 | 0 | 0 |
| Midterm Examinations (including preparation) | 2 | 6 | 12 |
| Project | 0 | 0 | 0 |
| Laboratory | 0 | 0 | 0 |
| Other Applications | 0 | 0 | 0 |
| Final Examinations (including preparation) | 1 | 16 | 16 |
| Quiz | 0 | 0 | 0 |
| Term Paper/ Project | 0 | 0 | 0 |
| Portfolio Study | 0 | 0 | 0 |
| Reports | 0 | 0 | 0 |
| Learning Diary | 0 | 0 | 0 |
| Thesis/ Project | 0 | 0 | 0 |
| Seminar | 0 | 0 | 0 |
| Other | 0 | 0 | 0 |
| Total Workload | 96 | ||
| Total Workload / 25 | 3,84 | ||
| Credits ECTS | 4 | ||