EM0019 Linear Programming

6 ECTS - 3-0 Duration (T+A)- . Semester- 3 National Credit

Information

Code EM0019
Name Linear Programming
Term 2024-2025 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

Update Time: 28.05.2024 02:15