To learn the basic stochastic modeling techniques, to develop Markov models of simple real life situations and gain insights on real life stochastic phenomena
Prerequisite(s)
IE3101 Introduction to Probability
Corequisite(s)
None
Special Requisite(s)
None
Instructor(s)
Assist. Prof. Dr. Duygun Fatih Demirel
Course Assistant(s)
Dilek Akburak
Schedule
This course is not offered in this semester.
Office Hour(s)
This course is not offered in this semester.
Teaching Methods and Techniques
-Lecture, question-answer, discussion, problem solving
Principle Sources
-Wayne L. Winston, Operations Research: Applications and Algorithms, 4th edition, Cengage Learning
-Hillier and Liebermannn, Itroduction to Operations Research, 8th edition, McGraw Hill
Other Sources
-
Course Schedules
Week
Contents
Learning Methods
1. Week
Deterministic Dynamic Programming
Lecture, question-answer, discussion, problem solving
2. Week
Deterministic Dynamic Programming (Cont’d)
Lecture, question-answer, discussion, problem solving
3. Week
Probabilistic Dynamic Programming
Lecture, question-answer, discussion, problem solving
4. Week
Probabilistic Dynamic Programming (Cont’d)
Lecture, question-answer, discussion, problem solving
5. Week
Stochastic Processes and Discrete Time Markov Chains (DTMCs), One Step Transition Probabilities
Lecture, question-answer, discussion, problem solving
6. Week
n-step transition probabilities, C-K equations, and unconditional state probabilities in DTMCs
Lecture, question-answer, discussion, problem solving
7. Week
Long-term behavior of DTMCs
Lecture, question-answer, discussion, problem solving
8. Week
Midterm
9. Week
Absorption probabilities in DTMCs, Work Force Planning Models
Lecture, question-answer, discussion, problem solving
10. Week
Continuous Time Markov Chains (CTMCs), and Exponential Distribution
Lecture, question-answer, discussion, problem solving
11. Week
Properties of Exponential Distribution and Poisson Process
Lecture, question-answer, discussion, problem solving
Lecture, question-answer, discussion, problem solving
13. Week
Queueing Theory, M/M/s Finite and Infinite Capacity Models
Lecture, question-answer, discussion, problem solving
14. Week
Network of Queues, Special Queue Systems
Lecture, question-answer, discussion, problem solving
15. Week
Final
16. Week
Final
17. Week
Final
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
35
Quizzes
4
10
Project(s)
1
10
Attendance
14
5
Final Exam
1
40
Program Outcomes
PO-1
Ability to apply theoretical and practical knowledge gained by Mathematics, Science and their engineering fields and ability to use their knowledge in solving complex engineering problems.
PO-2
Ability of determining, defining, formulating and solving complex engineering problems; for that purpose develop the ability of selecting and implementing suitable models and methods of analysis.
PO-3
Ability of designing a complex system, process, device or product under real world constraints and conditions serving certain needs; for this purpose ability of applying modern design techniques
PO-4
Ability of selecting and using the modern techniques and devices which are necessary for analyzing and solving complex problems in engineering implementations; ability of efficient usage of information technologies.
PO-5
Ability of designing experiments, conducting tests, collecting data and analyzing and interpreting the solutions to investigate of complex engineering problems or discipline-specific research topics.
PO-6
Ability of working efficiently in intra-disciplinary and multi-disciplinary teams; individual working ability and habits.
PO-7
Ability of verbal and written communication skills; and at least one foreign language skills, ability to write effective reports and understand written reports, ability to prepare design and production reports, ability to make impressive presentation, ability to give and receive clear and understandable instructions
PO-8
Awareness of importance of lifelong learning; ability to access data, to follow up the recent innovation in science and technology for continuous self-improvement.
PO-9
Conformity to ethical principles; knowledge about occupational and ethical responsibility, and standards used in engineering applications.
PO-10
Knowledge about work life implementations such as project management, risk management and change management; awareness about entrepreneurship and innovativeness; knowledge about sustainable development.
PO-11
Knowledge about effects of engineering applications on health, environment and security in global and social dimensions, and on the problems of the modern age in engineering; awareness about legal outcomes of engineering solutions.
Learning Outcomes
LO-1
Formulates deterministic and probabilistic Dynamic Programming problems, represents as a network, and solves the problem by working backwards.
LO-2
Models a given Problem as a Discrete Time Markov Chain (DTMC), writes down its one step and n-step transition matrices, computes long-term state probabilities of a DTMC, absorption probabilities, and interprets them.
LO-3
Explains the Exponential distribution and its relationship to the Poisson Process, and memoryless property.
LO-4
Writes down rate in and rate out equations of a CTMC and solves them in order to compute long-term probabilities of a CTMC.
LO-5
Explains the basic characteristics of M/M/1, M/M/s, finite and infinite capacity queuing systems, computes relevant performance measures, and interprets them.
LO-6
Gains the ability to use the necessary software in the application of the theoretical subjects learned in the course on real-life problems.
