 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 Spring 3 0 3 9
 This catalog is for information purposes. Course status is determined by the relevant department at the beginning of semester.

### Basic information

 Language of instruction: English Type of 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