IE 353 | Course Introduction and Application Information

Course Name
Optimization III-Stochastic Models
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
IE 353
Fall/Spring
3
0
3
8

Prerequisites
  IE 251 To succeed (To get a grade of at least DD)
and IE 240 To succeed (To get a grade of at least DD)
or MATH 240 To succeed (To get a grade of at least DD)
Course Language
English
Course Type
Elective
Course Level
First Cycle
Course Coordinator
Course Lecturer(s)
Assistant(s) -
Course Objectives Most systems and processes of organizations operating in almost all kinds of sectors (private/public, service/manufacturing etc.) are stochastic in nature. The objective of this course is to give the students the analytical skills and knowledge related to stochastic processes and models necessary to improve the systems and processes used in varying organizations.
Course Description The students who succeeded in this course;
  • Model any process as a stochastic one, analyze it and predict its evolution over time.
  • Provide a solution to new problems using the underlying theory of stochastic processes.
  • Classify the stochastic processes models.
  • Derive the fundamental equations of stochastic models.
  • Compare and contrast the models and techniques used in stochastic processes with those of other industrial engineering/operations research tools.
Course Content The course involves defining and modelling a stochastic process and solving the problems related to the stochastic process being investigated. After briefly discussing the theory, example problems will be solved related to each stochastic model. The main focus will be on the modelling and solving the problem.

 



Course Category

Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Related Preparation
1 Review of probability Winston, ch. 12, Ross, ch. 1-3
2 Discrete-time Markov chains – Chapman - Kolmogorov equations, limiting values of transition probabilities Winston, ch. 17, Ross, ch. 4
3 Discrete-time Markov chains – gambler’s ruin problem, mean time spent in transient states, branching processes Winston, ch. 17, Ross, ch. 4
4 Discrete-time Markov chains – Markov decision processes Poisson süreci – properties of exponential distribution Winston, ch. 17, 20, Ross, ch. 4-5
5 Poisson process – interarrival and waiting time distributions Ross, ch. 5
6 Poisson process – nonhomogeneous and compound poisson process Ross, ch. 5
7 Continuous-time Markov chains – birth and death processes Ross, ch. 6
8 Continuous-time Markov chains – transition probability function, computing the transition probabilities Ross, ch. 6
9 Renewal theory – distribution of the number of arrivals by time t, limit theorems, renewal reward processes Ross, ch. 7
10 Renewal theory – regenerative processes, computing the renewal function Ross, ch. 7
11 Queueing theory – cost equations, steady-state probabilities, M/G/1 model Winston, ch. 20, Ross, ch. 8
12 Queueing theory – G/M/1 model, multiserver queues Winston, ch. 20, Ross, ch. 8
13 Brownian motion – hitting times, brownian motion with drift Ross, ch. 10
14 Brownian motion – applications in finance Ross, ch. 10
15 Review of the semester
16 Final Exam

 

Course Notes/Textbooks

Wayne L. Winston, Operations Research: Applications and Algorithms, (International Student Edition), 4th edition, Brooks/Cole, 2004.

ISBN: 0-534-42362-0

Suggested Readings/Materials

Sheldon Ross, Introduction to Probability Models, 11th edition, Academic Press, 2014.

ISBN: 978-0124079489

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
Homework / Assignments
6
25
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
30
Final / Oral Exam
1
45
Total

Weighting of Semester Activities on the Final Grade
7
55
Weighting of End-of-Semester Activities on the Final Grade
1
45
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
Including exam week: 16 x total hours
16
3
48
Laboratory / Application Hours
Including exam week: 16 x total hours
16
Study Hours Out of Class
16
8.6
Field Work
Quizzes / Studio Critiques
Homework / Assignments
6
8
Presentation / Jury
Project
Seminar / Workshop
Portfolios
Midterms / Oral Exams
1
3
Final / Oral Exam
1
3
    Total
239.6

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 Adequate knowledge in Mathematics, Science and Software Engineering; ability to use theoretical and applied information in these areas to model and solve Software Engineering problems
2 Ability to identify, define, formulate, and solve complex Software Engineering problems; ability to select and apply proper analysis and modeling methods for this purpose
3 Ability to design, implement, verify, validate, measure and maintain a complex software system, process or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern methods for this purpose
4 Ability to devise, select, and use modern techniques and tools needed for Software Engineering practice
5 Ability to design and conduct experiments, gather data, analyze and interpret results for investigating Software Engineering problems
6 Ability to work efficiently in Software Engineering disciplinary and multi-disciplinary teams; ability to work individually
7 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of two foreign languages
8 Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9 Awareness of professional and ethical responsibility
10 Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development
11 Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of Software Engineering solutions

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest