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Information
| Code | TS540 |
| Name | Optimization II |
| Term | 2023-2024 Academic Year |
| Semester | . Semester |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Doktora Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator |
Course Goal / Objective
Primary objectives of this course are to: 1) put into make advanced linear models and their applications, 2) introduce LP Package programs, 3) interpret the results of different optimization techniques, 4) apply some optimization methods and algorithms selected in accordance with the needs of the students to the problems in daily life.
Course Content
Introduction; system concept; linear programming; geometric solution of linear programming, non-negative slack variables; dummy variables; Simplex algorithm of Dantzig, duality, sensitivity analysis; transportation problems
Course Precondition
In order to take this course, it is sufficient to be a graduate or doctoral student. However; Students who have prior knowledge about matrices, finding the minimum and maximum of functions can understand this lesson more easily and can be more successful than the others.
Resources
1. Taha, H. A., 2017. Operations Research - An Introduction. Tenth Edition (Global Edition), Pearson Education Limited. 2. Aladağ, Z., 2016. Yöneylem Araştırması. Umuttepe Yayınları, ISBN NO: 9786055100803. 3. Apaydın, A., 2005. Optimizasyon. Kılavuz Kitabevi, 4. Azimli, A., 2011. Matematiksel Optimizasyon. Papatya Yayıncılık Eğitim. 5. Bal, H., 1995. Optimizasyon Teknikleri. Gazi Üniversitesi Yayınları. 6. Bazaraa, M.S., Jarvis, J.J., Sherall, H. D., 1990. Linear Programming and Network Flows. John Wiley and Sons (2nd Edition) 7. Taha, H.A., 2003. Yöneylem Araştırması. Literatür Yayıncılık (6. Basımdan Çeviri) 8. Tecim, V., 2011. Yöneylem Araştırması. Lord Matbaacılık. 9. Winston, W. L., 2004. Operations Research Applications and Algorithms. Thomson Learning (Fourth Edition).
Notes
Selected articles from national and international journals.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Learns system concept. |
| LO02 | Solves a given set of simple optimization equations graphically. |
| LO03 | Helps students increase their ability to formulate problems mathematically. |
| LO04 | Interprets the unique and infinitely optimal solutions of an optimization problem. |
| LO05 | Allocates optimally the resources to the sectors by applying optimization techniques to practice. |
| LO06 | Gains the ability to interpret the meaning of maximization and minimization problems in terms of buyers and sellers. |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Has the ability to develop and deepen the level of expertise degree qualifications based on the knowledge acquired in the field of agriculture and irrigation structures | 3 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Has the ability to understand the interaction between irrigation and agricultural structures and related disciplines | |
| PLO03 | Bilgi - Kuramsal, Olgusal | Qualified in devising projects in agricultural structures and irrigation systems. | 2 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Conducts land applications,supervises them and assures of development | |
| PLO05 | Bilgi - Kuramsal, Olgusal | Has the ability to support his specilist knowledge with qualitative and quantitative data. Can work in different disciplines. | |
| PLO06 | Bilgi - Kuramsal, Olgusal | Solves problems by establishing cause and effect relationship | 5 |
| PLO07 | Bilgi - Kuramsal, Olgusal | Has the ability to apply theoretical and practical knowledge in the field of agricultural structures and irrigation department | 4 |
| PLO08 | Bilgi - Kuramsal, Olgusal | Able to carry out a study independently on a subject. | |
| PLO09 | Bilgi - Kuramsal, Olgusal | Has the ability to design and apply analytical, modelling and experimental researches, to analyze and interpret complex issues occuring in these processes. | 5 |
| PLO10 | Beceriler - Bilişsel, Uygulamalı | Can access resources on his speciality, makes good use of them and updates his knowledge constantly. | |
| PLO11 | Yetkinlikler - Öğrenme Yetkinliği | Has the ability to use computer software in agricultural structures and irrigation; can use informatics and communications technology at an advanced level. | 4 |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to optimization techniques | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Tartışma |
| 2 | System and system concept, some examples | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Beyin Fırtınası |
| 3 | Introduction to linear programming; matrices and basic properties of matrices | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Problem Çözme, Beyin Fırtınası |
| 4 | Basics/fundamentals of linear programming, mathematical forms | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Tartışma, Gösterip Yaptırma |
| 5 | Geometric solution of linear programming problems | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Geometric solution of linear programming (Continued): Single/unique optimal solution and infinitely optimal solution spaces | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Benzetim |
| 7 | Slack variables and their importance - Adding/Inserting to the system of equations | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Beyin Fırtınası |
| 8 | Mid-Term Exam | Textbooks, articles, Internet resources, supplemental documents | Ölçme Yöntemleri: Yazılı Sınav, Proje / Tasarım |
| 9 | Basic definitions and simplex based solution methods | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Problem formulation related to agriculture, environment, water resources, etc. and solutions | Textbooks and scientific articles | Öğretim Yöntemleri: Alıştırma ve Uygulama, Gösterip Yaptırma, Tartışma |
| 11 | Duality (optimization) | Textbooks, articles and Internet resources | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Sensitivity analysis | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Soru-Cevap, Tartışma |
| 13 | Transportation problems | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Benzetim, Problem Çözme, Beyin Fırtınası |
| 14 | Solving Nonlinear Equations o Newton-Raphson Method | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Benzetim, Gösterip Yaptırma |
| 15 | Solution of Equality Constrained Multivariate Optimization Problems o Lagrangian Method | Textbooks, articles and Internet resources; some open source programs | Öğretim Yöntemleri: Anlatım, Alıştırma ve Uygulama, Gösterip Yaptırma, Tartışma |
| 16 | Term Exams | Textbooks, articles, Internet resources, supplemental documents | Ölçme Yöntemleri: Yazılı Sınav, Proje / Tasarım |
| 17 | Term Exams | Textbooks, articles, Internet resources, supplemental documents | Ölçme Yöntemleri: Yazılı Sınav, Proje / Tasarım |
Student Workload - ECTS
| Works | Number | Time (Hour) | Workload (Hour) |
|---|---|---|---|
| Course Related Works | |||
| Class Time (Exam weeks are excluded) | 14 | 3 | 42 |
| Out of Class Study (Preliminary Work, Practice) | 14 | 5 | 70 |
| Assesment Related Works | |||
| Homeworks, Projects, Others | 0 | 0 | 0 |
| Mid-term Exams (Written, Oral, etc.) | 1 | 15 | 15 |
| Final Exam | 1 | 30 | 30 |
| Total Workload (Hour) | 157 | ||
| Total Workload / 25 (h) | 6,28 | ||
| ECTS | 6 ECTS | ||