Applied Mathematical Modeling(IND375)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| IND375 | Applied Mathematical Modeling | 6 | 3 | 0 | 0 | 3 | 4 |
| Prerequisites | IND371 |
| Admission Requirements | IND371 |
| Language of Instruction | French |
| Course Type | Elective |
| Course Level | Bachelor Degree |
| Course Instructor(s) | EBRU ANGÜN ebru.angun@gmail.com (Email) |
| Assistant | |
| Objective |
This course introduces several different types of mathematical models, which can be used to formulate real-life problems, and the softwares GAMS and MATLAB, which can be used to solve different types of problems including linear, non-linear, integer, etc. The aim is to introduce the logic of modeling, which can further be useful for academic studies and in industry. Hence, the objectives of the course are determined as follows: • Introduce how to build mathematical models of the real-life problems. • Enable students to use the softwares GAMS and MATLAB for programming and optimization. • Enable students to analyze and interpret the results of the optimization. |
| Content |
Introduction to GAMS and solution of a simple transportation problem through GAMS Modeling of linear programming problems (Bazaraa, Jarvis & Sherali, Chapter 1, Bertsimas & Tsitsiklis, Chapter 1) and solving linear programming problems through GAMS Sensitivity analysis in linear optimization and analysis of the results of GAMS (Bazaraa, Jarvis & Sherali, Chapter 6) Modeling of integer and mixed integer programming problems (Wolsey, Chapter 1) and solving these problems through GAMS Introduction to MATLAB and the optimization toolbox Introduction to quadratic programming (Fletcher, Chapter 2) and solving these problems through MATLAB, Markowitz Portfolio Model Introduction to unconstrained non-linear optimization (Fletcher, Chapter 2) and solving these problems through MATLAB Karush-Kuhn-Tucker optimality conditions, Lagrange multipliers, and applications for quadratic programming (Fletcher, Chapter 9) Modeling of stochastic programming problems (Birge & Louveaux, Chapter 1) and solving these problems through GAMS |
| Course Learning Outcomes |
Upon successful completion of this course, the student will be able to LO 1: Formulate real-life problems through mathematical models. LO 2: Give examples of different types of mathematical programming problems. LO 3: Solve different types of mathematical programming problems through professional softwares. LO 4: Model a real-life problem through different types of models and analyze the results. LO 5: Program in MATLAB and in GAMS to solve a mathematical model if necessary. LO 6: Analyze the results of the optimization. LO 7: Integrate the randomness to a mathematical model. LO 8: Work efficiently in a team to model a real-life problem and solve the resulting problem. |
| Teaching and Learning Methods |
Explain the subjects in class Encourage students to discuss Show how to program in GAMS and MATLAB Ask questions during the lecture Project |
| References |
Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., “Linear Programming and Network Flows”, 4. Edition, Wiley, New Jersey, 2010 Bertsimas, D., Tsitsiklis, J.N., “Introduction to Linear Optimization”, Athena Scientific Series in Optimization and Neural Computation, Massachusetts, 1997 Wolsey, L.A., “Integer Programming”, Wiley, New Jersey, 1998 Fletcher, R., “Practical Methods of Optimization”, 2. Edition, Wiley, Chichester, 2000 Birge, J.R., Louveaux, F., “Introduction to Stochastic Programming”, Springer, New York, 1997 Williams, H.P., “Model Building in Mathematical Programming”, 6. Edition, Wiley, Chichester, 2013 GAMS Manual, downloadable from http://www.gams.com/ |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Introduction to GAMS and solution of a simple transportation problem through GAMS |
| 2 | Modeling of linear programming problems (Bazaraa, Jarvis & Sherali, Chapter 1, Bertsimas & Tsitsiklis, Chapter 1) and solving linear programming problems through GAMS |
| 3 | Modeling of linear programming problems (Williams, Part 2) and solving linear programming problems through GAMS |
| 4 | Sensitivity analysis in linear optimization and analysis of the results of GAMS (Bazaraa, Jarvis & Sherali, Chapter 6) |
| 5 | Modeling of integer and mixed integer programming problems (Wolsey, Chapter 1) and solving these problems through GAMS |
| 6 | Modeling of integer and mixed integer programming problems (Williams, Part 2) and solving these problems through GAMS |
| 7 | Introduction to MATLAB and the optimization toolbox |
| 8 | Midterm |
| 9 | Introduction to quadratic programming (Fletcher, Chapter 2) and solving these problems through MATLAB, Markowitz Portfolio Model |
| 10 | Introduction to unconstrained non-linear optimization (Fletcher, Chapter 2) and solving these problems through MATLAB |
| 11 | Introduction to unconstrained non-linear optimization (Fletcher, Chapter 2) and solving these problems through MATLAB |
| 12 | Karush-Kuhn-Tucker optimality conditions, Lagrange multipliers, and applications for quadratic programming (Fletcher, Chapter 9) |
| 13 | Modeling of stochastic programming problems (Birge & Louveaux, Chapter 1) and solving these problems through GAMS |
| 14 | Modeling of stochastic programming problems (Birge & Louveaux, Chapter 1) and solving these problems through GAMS |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 2 | 60 |
| Contribution of final exam to overall grade | 1 | 40 |
| Toplam | 3 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 1 | 30 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 0 | 0 |
| Term Paper/ Project | 0 | 0 |
| Portfolio Study | 0 | 0 |
| Reports | 0 | 0 |
| Learning Diary | 0 | 0 |
| Thesis/ Project | 0 | 0 |
| Seminar | 0 | 0 |
| Other | 0 | 0 |
| Toplam | 2 | 60 |
| No | Program Learning Outcomes | Contribution | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | Knowledge and understanding of a wide range of basic sciences (math, physics, ...) and the main concepts of engineering | X | ||||
| 2 | Ability to combine the knowledge and skills to solve engineering problems and provide reliable solutions | X | ||||
| 3 | Ability to select and apply methods of analysis and modeling to ask, reformulate and solve the complex problems of industrial engineering | X | ||||
| 4 | Ability to conceptualize complex systems, processes or products under practical constraints to improve their performance, ability to use innovative methods of design | X | ||||
| 5 | Ability to design, select and apply methods and tools needed to solve problems related to the practice of industrial engineering, ability to use computer technology | X | ||||
| 6 | Ability to design experiments, collect and interpret data and analyze results | |||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | X | ||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | X | ||||
| 9 | Awareness of the need for continuous improvement of lifelong learning, ability to keep abreast of scientific and technological developments to use the tools of information management | |||||
| 10 | Awareness of professional and ethical responsibility | |||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | |||||
| 12 | Knowledge on entrepreneurship, innovation and sustainability | |||||
| 13 | Understanding of the effects of Industrial Engineering applications on global and social health, environment and safety. | |||||
| 14 | Knowledge of the problems of contemporary society | |||||
| 15 | Knowledge of the legal implications of the practice of industrial engineering | |||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 3 | 42 |
| Midterm Examinations (including preparation) | 1 | 8 | 8 |
| Project | 1 | 30 | 30 |
| Final Examinations (including preparation) | 1 | 12 | 12 |
| Total Workload | 92 | ||
| Total Workload / 25 | 3,68 | ||
| Credits ECTS | 4 | ||