Operations Research II

Course Code:

ISE 323

Course Period:

Autumn

Course Type:

Core

Credits:

4

Theoric:

3

Practice:

2

Laboratory Hour:

3

ECTS:

7

Prerequisite Courses:

Probability

Statistical Applications for Industrial Engineers

Course Language:

English

Courses given by:

Melek Başak

Course Objectives:

This is an introductory course designed to introduce the basic concepts and properties of modeling and analysis of probabilistic systems and the student is introduced the means of identifying, formulating and analyzing simple probabilistic models that are commonly faced in engineering practice. SYE 323 is planned for undergraduate students and intends to develop intuition and model building skills.

Course Content:

1. Probability Theory Review: Probability Theory basics including discrete and continuous Random Variables, Conditional Probability and Conditional Expectations.

2. Markov Chains: Basics, Chapman-Kolmogorov Equations, Limiting Probabilities and applications including Absorbing Chains, Work-Force Planning Models.

3. Exponential Distribution & Poisson Processes: Exponential Distribution and its Properties, Counting Processes, Poisson Processes, Generalization of Poisson Processes.

4. Queuing Theory: Preliminaries, M/M/1 systems with finite or infinite capacity, Network of Queues.

Course Methodology:

1: Lecture, 2: Question-Answer, 3: Lab, 4: Case-study

Course Evaluation Methods:

A: Testing, B: Experiment, C: Homework, D: Project

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Course Learning Outcomes

Course Learning Outcomes	Program Learning Outcomes	Teaching Methods		Assessment Methods
Remembers the basic concepts in probability theory.	1,2		1,2,4	A,C
Recognizes the basic properties of discrete and continuous random variables	1,2		1,2,4	A,C
Recognizes the characteristics of major random distributions. Identifies similarities and differences between these random distributions.	1,2		1,2,4	A,C
Describes the stochastic process and identifies the distinctive characterization of Markov Chains. Classifies the states in a MC process and determines the conditions for limiting probabilities to exist. Performs limiting probability problem applications.	1, 2, 3,6		1,2,4	A,C
Recognizes the concepts related to Counting process and Poisson processes and applies those concepts to model and to solve practical situations	1,2, 3		1,2,4	A,C
Describes the characteristic properties of an exponential M/M/1 queueing system both for finite and infinite capacity. Formulates the balance equaltions. Applies these to model and solve individual exponential system and network problems.	1,2,3,6		1,2,4	A,C

Course Flow

COURSE CONTENT
Week	Topics	Study Materials
1	Probability Theory Review: Random experiment, Axioms of probability Conditional Probability, Independence	Textbooks, lecture notes
2	Probability Theory Review: Discrete random variables Continuous random variables	Textbooks, lecture notes
3	Probability Theory Review: Expectation, Jointly distributed random variables, Independent random variables, Covariance and Correlation	Textbooks, lecture notes
4	Probability Theory Review and Markov Chains: Conditional Probability, Computing Expectations and Probabilities by conditioning Markov Chains : Introduction	Textbooks, lecture notes
5	Markov Chains: Chapman-Kolmogorov Equations, States	Textbooks, lecture notes
6	Markov Chains: Steady State probabilities Applications.	Textbooks, lecture notes
7	The Exponential Distribution & Poisson Processes: Counting processes	Textbooks, lecture notes
8	Exponential Distribution & Poisson Processes: Poisson Processes, Generalized Poisson processes	Textbooks, lecture notes
9	Review and Midterm I	Textbooks, lecture notes
10	Queuing Theory: Basics and Exponential Queuing Models	Textbooks, lecture notes
11	Queuing Theory: Exponential Queuing Models, infinite and finite capacity models	Textbooks, lecture notes
12	Queuing Theory: Finite capacity models	Textbooks, lecture notes
13	Review and Midterm II	Textbooks, lecture notes
14	General review

Recommended Sources

RECOMMENDED SOURCES

Textbooks

Introduction to Probability Models by Sheldon ROSS

Academic Press. ISBN 0-12-598061-2

Operations Research: Applications&Algorithms by W.L. Winston

Thomson, ISBN 0-534 42362-0.

Additional Resources

None

Material Sharing

MATERIAL SHARING
Documents
Assignments	5 assignments
Exams	5 Quizzes 2 Mid-term Examinations 1 Final Examination

Assessment

ASSESSMENT
IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	2	70
Assignments &Quizzes	10	30
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		40
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		60
Total		100

Course’s Contribution to Program

COURSE'S CONTRIBUTION TO PROGRAM
No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	Adequate background in Mathematics, Natural Sciences and the Industrial and Systems Engineering discipline.					X
2	Ability to identify, model and solve complex problems in the area of Industrial and Systems Engineering.					X
3	Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired requirements.					X
4	Ability to employ information technologies effectively in Industrial and Systems Engineering applications and develop and/or use modern techniques and tools for these applications.
5	Ability to design and conduct experiments and interpret results to analyze problems in the area of Industrial and Systems Engineering.
6	Ability to take responsibility both individually and as a team member to solve unforeseen problems that arise in intra-disciplinary and inter-disciplinary projects.			X
7	Ability to access information in the area of Industrial and Systems Engineering and to report and communicate this information to others using a foreign language (English) at the European Language Portfolio C1 General Level.
8	Ability to follow current issues and recent developments in science and technology by accessing databases and other sources of information and to continue to educate oneself.
9	Awareness of scientific and ethical responsibility in professional matters.
10	Ability to initiate innovative projects in the area of Industrial and Systems Engineering and to manage these projects considering all aspects.
11	Ability to identify the impact of Industrial and Systems Engineering applications on health, environment and safety; awareness of the legal consequences of Industrial and Systems Engineering solutions.

ECTS

ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (Excluding the exam weeks: 12x Total course hours)	14	3	42
	12	2	24
Hours for off-the-classroom study (Pre-study, practice)	14	5	70
Midterm examination	2	2	4
Homework	5	4	20
Quiz	5	0.5	2.5
Final examination	1	2	2
Total Work Load			164.5
Total Work Load / 25 (h)			6.6
ECTS Credit of the Course			7

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