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Information
| Code | EM511 |
| Name | Mathematical Modelling and Optimization |
| Term | 2024-2025 Academic Year |
| Term | Fall |
| Duration (T+A) | 3-0 (T-A) (17 Week) |
| ECTS | 6 ECTS |
| National Credit | 3 National Credit |
| Teaching Language | Türkçe |
| Level | Yüksek Lisans Dersi |
| Type | Normal |
| Mode of study | Yüz Yüze Öğretim |
| Catalog Information Coordinator | Prof. Dr. ALİ KOKANGÜL |
| Course Instructor |
1 |
Course Goal / Objective
The aim of this course is to provide detailed information on mathematical programming techniques and to help students gain ability to apply these techniques using LINDO package program.
Course Content
Mathematical models used in optimization problems, numerical methods for unconstrained optimization problems with one variable, numerical methods for constrained optimization problems with one variable, numerical methods for unconstrained optimization problems with multi-variable, numerical methods for constrained optimization problems with multi-variable, applications of mathematical models,project presentation.
Course Precondition
None
Resources
INTRODUCTION TO OPERATIONS RESEARCH, SEVENTH EDITION, Hillier/ Lieberman
Notes
Operations Research. Murthy, P.R.
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | To be able to set a mathematical model of any real life problem |
| LO02 | Choosing the most appropriate mathematical modeling approach |
| LO03 | Testing the validity of the model |
| LO04 | To gain the ability of using the solution derivation, application and LINGO package program |
| LO05 | To derive the solution in the model's computer package program |
Relation with Program Learning Outcome
| Order | Type | Program Learning Outcomes | Level |
|---|---|---|---|
| PLO01 | Bilgi - Kuramsal, Olgusal | Conducts scientific research in industrial engineering, understands, interprets and applies knowledge in his/her field domain both in-depth and in-breadth. | 5 |
| PLO02 | Bilgi - Kuramsal, Olgusal | Acquires detailed knowledge for methods and tools of industrial engineering and their limitations. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Keeps up with the recent changes and applications in the field of Industrial Engineering and examines and learns these innovations when necessary. | 4 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identifies, gathers and uses necessary information and data. | 4 |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Has the ability to develop/propose new and/or original ideas and methods, propose new solutions for designing systems, components or processes. | 3 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Designs Industrial Engineering problems, develops new methods to solve the problems and applies them. | 5 |
| PLO07 | Beceriler - Bilişsel, Uygulamalı | Designs and performs analytical modeling and experimental research and analyze/solves complex matters emerged in this process. | 5 |
| PLO08 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Works in multi-disciplinary teams, take a leading role and responsibility and develop solutions for complex problems. | 4 |
| PLO09 | Yetkinlikler - Öğrenme Yetkinliği | Completes and applies the knowledge by using limited resources in scientific methods and integrates the knowledge in the field with the knowledge form various disciplines. | 5 |
| PLO10 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a foreign language in verbal and written communication at least B2 level of European Language Portfolio. | |
| PLO11 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Presents his/her research findings systematically and clearly in oral or written forms in national and international platforms. | 3 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Understands social and environmental implications of engineering practice. | |
| PLO13 | Yetkinlikler - Öğrenme Yetkinliği | Considers social, scientific and ethical values in data collection, interpretation and announcement processes and professional activities. |
Week Plan
| Week | Topic | Preparation | Methods |
|---|---|---|---|
| 1 | Introduction to mathematical programming | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 2 | Mathematical models used in optimization problems | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 3 | Unconstrained mathematical modeling techniques | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 4 | Constrained mathematical modeling techniques | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 5 | Numerical methods for unconstrained optimization problems with one variable I | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 6 | Numerical methods for constrained optimization problems with one variable II | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 7 | Numerical methods for unconstrained optimization problems with multi-variable I | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 8 | Mid-Term Exam | Preparation for the exam | Ölçme Yöntemleri: Yazılı Sınav |
| 9 | Numerical methods for unconstrained optimization problems with multi-variable II | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 10 | Numerical methods for constrained optimization problems with multi-variable I | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 11 | Numerical methods for constrained optimization problems with multi-variable II | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 12 | Applications of mathematical models I | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 13 | Applications of mathematical models II | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 14 | Project presentation I | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 15 | Project presentation | Preliminary research on the subject and investigation of current applications | Öğretim Yöntemleri: Anlatım, Soru-Cevap, Tartışma |
| 16 | Term Exams | Preparation for the exam | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Term Exams | Preparation for the exam | Ölçme Yöntemleri: Yazılı Sınav |
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 | ||