INE6101 Linear OptimizationBahçeşehir UniversityDegree Programs INDUSTRIAL ENGINEERING (ENGLISH, PHD)General Information For StudentsDiploma SupplementErasmus Policy StatementNational Qualifications
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
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


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
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