END502

School of Engineering \ Industrial Engineering

3

6

Elective

Turkish

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Elective
END - Industrial Engineering Master's Degree
BİL - Computer Engineering Master's Degree
ELE - Electrical Electronics Engineering Master's Degree
MAK - Mechanical Engineering Master's Degree
MBN - Materials Science and Nanotechnology Engineering Master's Degree
BMM - Biomedical Engineering Master's Degree
İKT - Economics Master's Degree
İŞL - Business Administration Master's Degree

1. Introduction to Integer Programming
2. Modeling Examples
3. Complexity Theory and Polyhedral Theory
4. Branch-and-Bound Algorithm
5. Valid Inequalities
6. Lagrangian Relaxation

1. Laurence A. Wolsey,Integer Programming, John Wiley and Sons, 1998.
2. G. L. Nemhauser and L. A. Wolsey,Integer and Combinatorial Optimization, Wiley, 1988.
3. A. Schrijver,Theory of Linear and Integer Programming, Wiley, 1986.

This course is a graduate level introductory course to integer programming, modeling, and optimization. The aim of the course is to provide students with a general perspective on integer programming models and the solution methods used for them.

1. Gain the ability to construct mathematical models of difficult problems, especially those encountered in real life, using integer variables and to determine the more "effective" model among alternative models;
2. Know the difference between "easy" and "difficult" problems,
3. Gain the ability to understand and apply solution techniques that can be used for integer programming models,
4. Gain the ability to read and critically examine academic articles in the literature,
5. Gain sufficient knowledge about theoretical topics such as valid inequalities, polyhedral theory, and decomposition methods.

Week 1: Fundamentals of Integer Programming
Week 2: Modeling
Week 3: Branch-and-Bound Algorithm
Week 4: Complexity Theory
Week 5: Polyhedral Theory
Week 6: Branching and Node Selection Techniques
Week 7: Valid Inequality Derivation Methods
Week 8: Lifting and Inclusion Inequalities
Week 9: Mixed Integer Rounding
Week 10: Lagrangian Relaxation
Week 11: Branch Price Method - Case Analysis
Week 12: Case Analysis

• Midterm 1 25 %
• Midterm 2 25 %
• Final 35 %
• Homework 15 %