| Course Description |
|
| Course Name |
: |
Linear Programming |
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| Course Code |
: |
MT 469 |
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| Course Type |
: |
Optional |
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| Level of Course |
: |
First Cycle |
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| Year of Study |
: |
4 |
|
| Course Semester |
: |
Fall (16 Weeks) |
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| ECTS |
: |
5 |
|
| Name of Lecturer(s) |
: |
Assoc.Prof.Dr. AHMET TEMİZYÜREK
|
|
| Learning Outcomes of the Course |
: |
Describes the properties of the linear programming problem
Creates a linear programming model and Solves the problem using solution methods such as graphical and analytical methods
Uses the Simplex Solution technique
Is aware of the diference between the Simplex method and the two-phase method
Uses the Two-Phase Method
Uses Big M Method
Is able to write dual of a linear model, distinguishes the Relations between the solutions of Main problems and Dual problems.
Is able to write Balanced and unbalanced transportation model and solves them.
Solves the Graph and assignment models.
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| Mode of Delivery |
: |
Face-to-Face |
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| Prerequisites and Co-Prerequisites |
: |
None |
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| Recommended Optional Programme Components |
: |
None |
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| Aim(s) of Course |
: |
To establish a model for Linear Programming Problems and to be able to solve the established problems with various momethods. To teach applications of linear programming in various areas. |
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| Course Contents |
: |
Introduction to linear programming and examples. Approaches for solutions of a linear programming problem: graphical approach, analytic approach. The simplex Method: the use of artificial variables, the two stage simplex algorithm. Duality, the theory of the dual simplex Method and its applications. The transportation problem and solution of a transportation problem. The relationship between game theory and linear programming.
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|
| Language of Instruction |
: |
Turkish |
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| Work Place |
: |
Classrooms Faculty of Arts and Sciences |
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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
|
1 |
Definitions and examples about Linear programming problems |
Review of the relevant pages from sources |
lectures and problem-solving |
|
2 |
Hyperplanes, Convex sets and linear functions over the convex sets |
Review of the relevant pages from sources |
lectures and problem-solving |
|
3 |
Geometric solutions |
Review of the relevant pages from sources |
lectures and problem-solving |
|
4 |
Gauss-Jordan reduction, Linear Programming Problems in Canonical form |
Review of the relevant pages from sources |
lectures and problem-solving |
|
5 |
Analytical solution |
Review of the relevant pages from sources |
lectures and problem-solving |
|
6 |
The Simplex Method |
Review of the relevant pages from sources |
lectures and problem-solving |
|
7 |
Two-Phase Method |
Review of the relevant pages from sources |
lectures and problem-solving |
|
8 |
mid term exam |
Review the topics discussed in the lecture notes and sources |
Written exam |
|
9 |
Two-Phase Method and The Big M Method |
Review of the relevant pages from sources |
lectures and problem-solving |
|
10 |
The dual of the linear model, Relationships between Solutions of the original and dual models. |
Review of the relevant pages from sources |
lectures and problem-solving |
|
11 |
Transportation models and solution techniques |
Review of the relevant pages from sources |
lectures and problem-solving |
|
12 |
Assignment model and Hungarian algorithm |
Review of the relevant pages from sources |
lectures and problem-solving |
|
13 |
Graph models and shortest route problems |
Review of the relevant pages from sources |
lectures and problem-solving |
|
14 |
Maximal flow problems |
Review of the relevant pages from sources |
lectures and problem-solving |
|
15 |
Maximal flow problems |
Review of the relevant pages from sources |
lectures and problem-solving |
|
16/17 |
Final exam |
Review the topics discussed in the lecture notes and sources |
Written exam |
|
|
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Required Course Resources |
| Resource Type | Resource Name |
| Recommended Course Material(s) |
 Optimizasyon, Ayşen Apaydın,A.Ü.F.F. press, 1996
Yöneylem Araştırması, Ahmet Öztürk, Ekin publishing house,2009
|
| |
| Required Course Material(s) |
Elementary Linear Programing With Applications, Bernard Kolman and Robert E. Beck, Academic Press,1980
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|
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| Contribution of the Course to Key Learning Outcomes |
| # | Key Learning Outcome | Contribution* |
|
1 |
Is able to prove Mathematical facts encountered in secondary school. |
4 |
|
2 |
Recognizes the importance of basic notions in Algebra, Analysis and Topology |
1 |
|
3 |
Develops maturity of mathematical reasoning and writes and develops mathematical proofs. |
3 |
|
4 |
Is able to express basic theories of mathematics properly and correctly both written and verbally |
5 |
|
5 |
Recognizes the relationship between different areas of Mathematics and ties between Mathematics and other disciplines. |
3 |
|
6 |
Expresses clearly the relationship between objects while constructing a model |
4 |
|
7 |
Draws mathematical models such as formulas, graphs and tables and explains them |
2 |
|
8 |
Is able to mathematically reorganize, analyze and model problems encountered. |
3 |
|
9 |
Knows at least one computer programming language |
2 |
|
10 |
Uses effective scientific methods and appropriate technologies to solve problems |
0 |
|
11 |
Knows programming techniques and is able to write a computer program |
0 |
|
12 |
Is able to do mathematics both individually and in a group. |
0 |
|
13 |
Has sufficient knowledge of foreign language to be able to understand Mathematical concepts and communicate with other mathematicians |
0 |
|
14 |
In addition to professional skills, the student improves his/her skills in other areas of his/her choice such as in scientific, cultural, artistic and social fields |
0 |
| * Contribution levels are between 0 (not) and 5 (maximum). |
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