INDUSTRIAL ENGINEERING (ENGLISH, PHD)
PhD	TR-NQF-HE: Level 8	QF-EHEA: Third Cycle	EQF-LLL: Level 8

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
INE6101	Linear Optimization	Fall	3	0	3	9

Basic information

Language of instruction:	English
Type of course:	Must Course
Course Level:
Mode of Delivery:	Face to face
Course Coordinator :
Course Lecturer(s):	Prof. Dr. SÜREYYA AKYÜZ Dr. Öğr. Üyesi YÜCEL BATU SALMAN
Recommended Optional Program Components:	N.A.
Course Objectives:	This course aims to formulate business problems as linear programming models, solve linear programming models by using simplex algorithm, understand the theory of simplex algorithm, analyze the relationship between the primal and dual problem, model problems as network optimization models, and analyze basic solution algorithms in network optimization.

Learning Outcomes

The students who have succeeded in this course;
I. Formulate mathematical models of business problems using linear programming and network theory.
II. Follow problem solution techniques such as simplex algorithm and understand the theory of simplex algorithm.
III. Analyze the usage and the limitations of simplex algorithm.
IV. Follow polynomial time solution algorithms for linear programming, such as Karmarkar's projective algorithm.
V. Use primal-dual relationships and examine economic interpretation of duality.
VI. Formulate network flow problems such as shortest path, maximum flow, minimum cost flow problems.
VII. Apply solution techniques for different network flow problems.

Course Content

This course provides a comprehensive overview of the principles and practice of optimization. Main focus of this course is on deterministic models with an emphasis on linear programming and network flows. The topics of this course include linear programming, theory of simplex algorithm, duality theory, network flows and algorithms.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	Linear programming modeling and examples
2)	Convex analysis and polyhedral sets
3)	Theory of Simplex method
4)	Simplex method- Starting solution
5)	Simplex method - special simplex implementations
6)	Optimality conditions, KKT conditions and Farka's Lemma
7)	Duality and sensitivity analysis
8)	Complexity of the Simplex algorithm and polynomial algorithms
9)	Midterm
10)	Network Flow Programming Models and Methods - Introduction
11)	Shortest path problem
12)	Maximum flow problem
13)	Minimum cost network problem
14)	Review

Sources

Course Notes / Textbooks:	Title: Linear Programming and Network Flows Authors: Mokhtar S. Bazaraa, John J. Jarvis and Hanif D. Sherali Published by: John Wiley & Sons Inc. ISBN: 0-471-48599-3
References:	Introduction to Linear Optimization Bertsimas, Dimitris, and Tsitsiklis, John N 1997 1-886529-19-1 Operations Research Models and Methods Paul A. Jensen and Jonathan F. Bard 2003 978-0-471-38004-7

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Homework Assignments	4	% 20
Midterms	1	% 30
Final	1	% 50
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 50
PERCENTAGE OF FINAL WORK		% 50
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	13	3	39
Study Hours Out of Class	2	35	70
Homework Assignments	4	20	80
Midterms	1	3	3
Final	1	3	3
Total Workload			195

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	To understand and implement areas that are related with basic sciences, mathematics, and industrial engineering at a high level.	3
2)	To have expanded and deeper knowledge in the related field including the most recent developments.	3
3)	To use and evaluate knowledge with a systematic approach.	4
4)	To have high level proficiency of necessary methods and skills to reach the latest knowledge in the field and to understand the knowledge for making research studies.	4
5)	To make a comprehensive study innovating science and technology, developing new scientific method or technological product/process, implementing a known method to a new field.
6)	To be able to detect, design, implement, and finalize an original independent research process; to manage this process
7)	To be able to contribute science and technology by publishing outcomes of academic studies in reputable scholarly environments.
8)	To be able to evaluate scientific, technological, social and cultural developments, and to transfer these developments to society with scientific objectivity and ethical responsibility.
9)	To be able to conduct critical analysis, synthesis and evaluation of thoughts and developments in focusing field.
10)	To be Able to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.
11)	To be able to conduct functional interaction to solve the problems related to the field by using the strategic decision making processes
12)	To have effective and efficient management capabilities