Mathematical Programming
Industrial Engineering
Institute of Natural and Applied Sciences
Second Cycle (Master's Degree)
| Course Unit Title | Course Unit Code | Type of Course Unit | Level of Course Unit | Year of Study | Semester | ECTS Credits |
|---|---|---|---|---|---|---|
| Mathematical Programming | MEN543 | Compulsory | Master's degree | 1 | Spring | 10 |
Name of Lecturer(s)
Assistant Prof. Dr. Yıldız ŞAHİN
Learning Outcomes of the Course Unit
1) To be able to identify problems and systems in different decision environments with variables, constraints and objectives,
2) To establish mathematical models of defined problems and systems
3) To be able to solve decision models by using algorithms and techniques
4) To make sensitivity analysis for solution results
5) To be able to use computer programs to solve decision models
6) To be able to conduct a literature study to examine current scientific research in mathematical programming
7) Solving and analyzing real life problems based on scientific based researches and methods
Program Competencies-Learning Outcomes Relation
| Program Competencies | ||||||
| 1 | 2 | 3 | 4 | 5 | ||
| Learning Outcomes | ||||||
| 1 | High | High | High | High | Middle | |
| 2 | High | High | High | Middle | No relation | |
| 3 | High | Low | High | Middle | No relation | |
| 4 | High | Middle | High | High | No relation | |
| 5 | High | No relation | High | Low | No relation | |
| 6 | High | No relation | Low | Low | No relation | |
| 7 | High | No relation | High | Middle | No relation | |
Mode of Delivery
Face to Face
Prerequisites and Co-Requisites
None
Recommended Optional Programme Components
Not Required
Course Contents
Mathematical models - Advanced linear programming - Graphical solution of the linear model and graphical analysis - Simplex method - Sensitivity analysis - Introduction to integer programming - Transportation problem - Principles of dynamic programming - Nonlinear optimization methods - Applications.
Weekly Schedule
1) Mathematical models, Linear programming2) Linear programming, Graphical solution and graphical analysis of the sensitivity of the linear model, examination of applications
3) Simplex method, Examination of applications
4) Simplex method, Sensitivity analysis, Examination of applications
5) Integer Programming, Transportation problem, examination of applications
6) Principles of dynamical programming, examination of applications
7) Non-linear methods of optimization, Applications
8) midterm exam
9) Nonlinear programming (NP), definition and graphical representation of NP problems (Literature review and presentation)
10) Classical optimization theory-unconstrained optimization (Literature review and presentation-presentation of project proposal)
11) Classical optimization theory-constrained optimization (Lagrange Method) (Literature review and presentation-presentation of project proposal)
12) Classical optimization theory-constrained optimization (Karush-Kuhn-Tucker Method) (Literature review and presentation-presentation of the project proposal)
13) Quadratic Programming (Literature review and presentation-presentation of project proposal)
14) Dynamic Programming (Literature review and presentation-presentation of project proposal)
15) Project presentations
16) Final Exam, Project Report Submission
Recommended or Required Reading
1- WINSTON, W.L., (2004), Operations Research: Applications and Algorithms Text Book (Student Edition) Fourth Edition, Brooks/Cole Publishing Co
2- TAHA, H. (2006), Operations Research: An Introduction, 8th Edition, Prentice Hall.
3- TAYLOR, B.W. (2009), Introduction to Management Science, 10th Edition, Prentice Hall.
Planned Learning Activities and Teaching Methods
1) Drill and Practice
2) Modelling
3) Group Study
4) Self Study
5) Problem Solving
Assessment Methods and Criteria
Contribution of Midterm Examination to Course Grade |
20% |
|---|---|
Contribution of Final Examination to Course Grade |
80% |
Total |
100% |
Language of Instruction
Other
Work Placement(s)
Not Required