SULEYMAN DEMIREL UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT of INFORMATION SYSTEMS
«CSS301 MODELS AND METHODS IN CONTROL THEORY»
3 credits
Explanatory note of course
This course will cover the very basic ideas in “models and methods in control theory”.
Topics include the basic theory and algorithms behind linear and integer linear programming
along with some of the important applications.
Linear Programming (LP) is arguably one of the most important optimization problems in
applied mathematics and engineering. The Simplex algorithm to solve linear programs is widely
regarded as one among the "top ten" algorithms of the 20th century. Linear Programs arise in
almost all fields of engineering including operations research, statistics, machine learning,
control system design, scheduling, formal verification and computer vision. It forms the basis for
numerous approaches to solving hard combinatorial optimization problems through
randomization and approximation.
Pre-requisites
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Linear algebra, geometry and discrete mathematics
Course goals and objectives
 A primary objective is to give students general knowledge of basics of optimization course.
 Understand the basic theory behind LP, algorithms to solve LPs, and the basics of (mixed)
integer programs.
 Understand important and emerging applications of LP to economic problems (optimal
resource allocation), diet problem, transportation problems, assignment problems, and so on.
At the end of the course, the successful student will be able to cast various problems that
may arise in her research as optimization problems, understand the cases where the
optimization problem will be linear, choose appropriate solution methods and interpret
results appropriately. This is generally considered a useful ability in many research areas.
Literature
1. “Operations Research: An Introduction”, Hamdy A. Taha.
2. “Введение в исследование операций”, Хэмди А. Таха.
3. “Математические методы и модели в управлении”, Е. В. Шикин, А. Г. Чхартишвили.
Contents of Course
SYLLABUS
Week #1:
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Introduction to Linear Programming.
Linear Programming Formulations.
How to Solve Linear Programs
Graphical method
Week #2:
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Algebraic method to solve Linear programming.
Week #3:
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The Simplex Algorithm (basics). Diet problem.
Week #4:
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More details on Simplex: Handling unbounded problems.
Initialization Phase Simplex.
Cycling and the Use of Bland's rule.
Complexity of Simplex.
Week #5:
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Big-M method to solve simplex method.
Week #6:
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Two phase method to solve simplex method.
Week #7 and 8:
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Duality: dual variables and dual linear program.
Strong duality theorem.
Complementary Slackness.
Understanding the dual problem: shadow costs.
Week #9:
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Transportation problem.
Northwest Corner cell method.
Least cost cell method.
Vogal’s Approximation method.
Week #10:
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Stepping Stone method for transportation problems.
Week #11:
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MODI method for transportation problems.
Week #12:
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Optimizing the basic feasible solution using U-V method in transportation problems.
Week #13 and 14:
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Assignment problem,
Hungarian algorithm.
Unbalanced Assignment Problems.
Topics for practical lessons
1- Linear Programming Formulations , problem solve by Graphical method
2- Algebraic method
3- Simplex method, Diet problem.
4- Solving Degeneracy and Cycling in simplex method, Use of Bland's rule.
5- Big-M method
6- Two-phase method
7- Duality, duality construction.
8- Northwest Corner cell method, Least cost cell method, Vogal’s Approximation method.
9- Stepping Stone method.
10- MODI method
11- Optimizing U-V method.
12- Hungarian algorithm.
Topics for student self study works
1. Graphical method
2. Algebraic method
3. Diet problem
4. Simplex method
5. Big-M method
6. Two-phase method
7. Construction of Duality
8. Northwest Corner cell, Least cost cell, Vogal’s Approximation methods.
9. Stepping Stone method
10. MODI method
11. Optimizing U-V method.
12. Hungarian algorithm.
Topics for student self study works with instructor
1- Diet problem
2- Stepping stone method. MODI method. Optimizing U-V method.
3- Hungarian algorithm.
Literature
1. “Operations Research: An Introduction”, Hamdy A. Taha.
2. “Введение в исследование операций”, Хэмди А. Таха.
3. “Математические методы и модели в управлении”, Е. В. Шикин, А. Г. Чхартишвили.