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Information
| Code | EM0019 |
| Name | Linear Programming |
| 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
This course aims to formulate business problems as linear programming models, solve linear programming models by using simplex algorithm, understand the theory of simplex algorithm, analyze the relationship between the primal and dual problem, model problems as network optimization models, and analyze basic solution algorithms in network optimization.
Course Content
This course provides a comprehensive overview of the principles and practice of optimization. Main focus of this course is on deterministic models with an emphasis on linear programming and network flows. The topics of this course include linear programming, theory of simplex algorithm, and duality theory.
Course Precondition
None
Resources
Hilller and Lieberman. Introduction to Operations Research. seventh Edition. Mcgraw Hill Book Company.2008
Notes
Hilller and Lieberman. Introduction to Operations Research. seventh Edition. Mcgraw Hill Book Company.2008
Course Learning Outcomes
| Order | Course Learning Outcomes |
|---|---|
| LO01 | Formulate mathematical models of business problems using linear programming |
| LO02 | Applying the simplex method theory method |
| LO03 | Evaluate the results with sensitivity analysis |
| LO04 | Applying the Duality Theorem |
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 | Keeps up with the recent changes and applications in the field of Industrial Engineering and examines and learns these innovations when necessary. | 4 |
| PLO03 | Bilgi - Kuramsal, Olgusal | Acquires detailed knowledge for methods and tools of industrial engineering and their limitations. | 5 |
| PLO04 | Bilgi - Kuramsal, Olgusal | Identifies, gathers and uses necessary information and data. | |
| PLO05 | Beceriler - Bilişsel, Uygulamalı | Develops original definitions that will provide innovation to the field at the level of expertise for current and advanced information in the field based on graduate qualifications. | 4 |
| PLO06 | Beceriler - Bilişsel, Uygulamalı | Designs and performs analytical modeling and experimental research and analyze/solves complex matters emerged in this process. | 5 |
| PLO07 | 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. | 4 |
| PLO08 | Beceriler - Bilişsel, Uygulamalı | Designs Industrial Engineering problems, develops new methods to solve the problems and applies them. | |
| PLO09 | Yetkinlikler - Bağımsız Çalışabilme ve Sorumluluk Alabilme Yetkinliği | Works in multi-disciplinary teams, take a leading role and responsibility and develop solutions for complex problems. | |
| PLO10 | 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. | 3 |
| PLO11 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Uses a foreign language in verbal and written communication at least B2 level of European Language Portfolio. | 4 |
| PLO12 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Presents his/her research findings systematically and clearly in oral or written forms in national and international platforms. | 4 |
| PLO13 | Yetkinlikler - İletişim ve Sosyal Yetkinlik | Understands social and environmental implications of engineering practice. | |
| PLO14 | 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 | Brief history of linear programming and introductory example | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 2 | General form of linear programming in canonical maximization form | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 3 | Conversions of constraints and variables | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 4 | Examples of linear programming formulation | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 5 | Examples of linear programming formulation-2 | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 6 | Convex sets and convex functions | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 7 | Convexity, hyperplanes, half-spaces | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 8 | Midterm Exam | Studying on books and lecture notes | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 9 | Extreme points of polyhedra, basic and basic feasible solutions | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 10 | Adjacent basic solutions, polyhedra in standard form and basic solutions for standard form | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 11 | Directions and unbounded LPs, extreme directions, representation theorem | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 12 | Simplex method explained in terms of basis matrices | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 13 | Simplex tableau in matrix form, alternative optima, unbounded solution | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 14 | Degeneracy and resolution of cycling | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 15 | Duality theorems | Reading the lecture notes and references related to the subject | Öğretim Yöntemleri: Anlatım, Soru-Cevap |
| 16 | Final Exam | Studying on books and lecture notes | Ölçme Yöntemleri: Yazılı Sınav |
| 17 | Final Exam | Studying on books and lecture notes | Ölçme Yöntemleri: Ödev |
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 | ||