| Course Name | Art of Mathematical Modelling |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| IE 355 | Fall/Spring | 2 | 2 | 3 | 6 |
| Prerequisites |
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| Course Language | English | ||||||||
| Course Type | Elective | ||||||||
| Course Level | First Cycle | ||||||||
| Mode of Delivery | - | ||||||||
| Teaching Methods and Techniques of the Course | |||||||||
| Course Coordinator | |||||||||
| Course Lecturer(s) | |||||||||
| Assistant(s) | - | ||||||||
| Course Objectives | The aim of this course is to teach students building mathematical models and heuristic solution algorithms of real-life problems and to enable them solving the complex problems encountered in business. |
| Learning Outcomes | The students who succeeded in this course;
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| Course Description | Topics of this course include developing mathematical models and heuristic solution algorithms for essential Industrial Systems Engineering problems. During the course, IBM ILOG OPL Development Studio will be used to code and solve mathematical models and heuristic algorithms. |
| Related Sustainable Development Goals | |
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| Core Courses | |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Introduction to Mathematical Modeling and OPL | IBM ILOG CPLEX OPTIMIZATION STUDIO (OPL) Documentation version 16, A Short Introduction to OPL |
| 2 | Building Linear Programming Models I : Workforce Planning | Winston, W. L., Operations Research: Applications and Algorithms, Ch 3, Duxbury Press |
| 3 | Building Linear Programming Models II: Supply planning and CPM models | Winston, W. L., Operations Research: Applications and Algorithms, Ch 8, Duxbury Press |
| 4 | Linearizing Logical Forms with Binary Variables, Quiz I | Sierksma, G. Linear and Integer Programming Theory and Practice, Ch 6, Marcel Dekker Inc. Second Edition |
| 5 | Building Integer Programming Models: Modeling integer programming models with conditional decisions, set packing, covering and partitioning problems | Hillier, F. S., and Lieberman, G. J., Introduction to Operations Research, Ch 11,Ninth Edition, 2010 Mc Graw-Hill |
| 6 | Algorithm development and programming with ILOG OPL | IBM ILOG CPLEX OPTIMIZATION STUDIO (OPL) Documentation version 16 |
| 7 | Quadratic Assignment Problem Model Formulations and Heuristic Solution Algorithms | Sierksma, G. Linear and Integer Programming Theory and Practice, Ch 6-7, Marcel Dekker Inc. Second Edition |
| 8 | Traveling Salesman Problem Model Formulations and Heuristic Solution Algorithms, Cutting Stock Problems | Hillier, F. S., and Lieberman, G. J., Introduction to Operations Research, Ch 13, Ninth Edition, 2010 Mc Graw-Hill |
| 9 | Industrial Applications of Integer Programming I : Lot Sizing and Scheduling Models, Wagner Whitin Algorithm, Vehicle Routing Problem | |
| 10 | Industrial Applications of Integer Programming II : Assembly Line Balancing , Dedicated Storage System Models and Heuristic Solution Algorithms | |
| 11 | Industrial Applications of Integer Programming III : Modeling Machine Scheduling Problems I : Single Machine and Job Shop Scheduling Problems | M. L. Pinedo, Scheduling: Theory, Algorithms, and Systems Ch 3-4, 2005, Springer, |
| 12 | Industrial Applications of Integer Programming IV : Modeling Machine Scheduling Problems II : Single Machine and Job Shop Scheduling Problems with sequence dependent setup times | M. L. Pinedo, Scheduling: Theory, Algorithms, and Systems Ch 3-4, 2005, Springer, |
| 13 | Industrial Applications of Integer Programming V : Modeling Machine Scheduling Problems III : Heuristic solution algorithms and constraint programming models to solve single machine and job shop scheduling problems | M. L. Pinedo, Scheduling: Theory, Algorithms, and Systems Ch 3-4, 2005, Springer, |
| 14 | Project Presentations, Quiz II | |
| 15 | Review of the semester | |
| 16 | Final Exam |
| Course Notes/Textbooks | Model Building in Mathematical Programming, Fourth ed., H. Paul Williams, WILEY. |
| Suggested Readings/Materials | Lecture PowerPoint slides, Reading Handouts, Articles from journals, Optimization in Operations Research, Ronald L.Rardin, Prentice Hall, ISBN : 0-02-398415-5, Introduction to Operations Research, Frederick S. Hillier, Gerald J. Lieberman, Ninth Edition, 2010 Mc Graw-Hill, ISBN: 978-007-126767-0 , Operations Research: Applications and Algorithms, Wayne L. Winston, Duxbury Press, ISBN 0-534 20971-8., Linear and Integer Programming Theory and Practice, Gerard Sierksma, Marcel Dekker Inc., Second Edition, ISBN 978-0824706739, Optimization Modeling A Practical Approach, Ruhul A. Sarker, Charles S. Newton, CRC Press, 2008, ISBN 978-1420043105, Applied Integer Programming, Modeling and Solution. Der-San Chen, Robert G. Batson, Yu Dang, Wiley, 2010. ISBN 978-0-470-37306-4, Logic and Integer Programming, H. Paul Williams, Springer, ISBN 978-0387922799, M. L. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2005, Springer, ISBN 978-0387789347, IBM ILOG CPLEX OPTIMIZATION STUDIO (OPL) Documentation. |
| Semester Activities | Number | Weigthing |
| Participation | 1 | 5 |
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | | |
| Portfolio | ||
| Homework / Assignments | 1 | 15 |
| Presentation / Jury | ||
| Project | 1 | 10 |
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 30 |
| Final Exam | 1 | 40 |
| Total |
| Weighting of Semester Activities on the Final Grade | 4 | 60 |
| Weighting of End-of-Semester Activities on the Final Grade | 1 | 40 |
| Total |
| Semester Activities | Number | Duration (Hours) | Workload |
|---|---|---|---|
| Course Hours (Including exam week: 16 x total hours) | 16 | 2 | 32 |
| Laboratory / Application Hours (Including exam week: 16 x total hours) | 16 | 2 | |
| Study Hours Out of Class | 14 | 3 | 42 |
| Field Work | |||
| Quizzes / Studio Critiques | | | |
| Portfolio | |||
| Homework / Assignments | 1 | 12 | |
| Presentation / Jury | |||
| Project | 1 | 22 | |
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 17 | |
| Final Exams | 1 | 23 | |
| Total | 180 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To have knowledge in Mathematics, science, physics knowledge based on mathematics; mathematics with multiple variables, differential equations, statistics, optimization and linear algebra; to be able to use theoretical and applied knowledge in complex engineering problems | |||||
| 2 | To be able to identify, define, formulate, and solve complex mechatronics engineering problems; to be able to select and apply appropriate analysis and modeling methods for this purpose. | |||||
| 3 | To be able to design a complex electromechanical system, process, device or product with sensor, actuator, control, hardware, and software to meet specific requirements under realistic constraints and conditions; to be able to apply modern design methods for this purpose. | |||||
| 4 | To be able to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in Mechatronics Engineering applications; to be able to use information technologies effectively. | |||||
| 5 | To be able to design, conduct experiments, collect data, analyze and interpret results for investigating Mechatronics Engineering problems. | |||||
| 6 | To be able to work effectively in Mechatronics Engineering disciplinary and multidisciplinary teams; to be able to work individually. | |||||
| 7 | To be able to communicate effectively in Turkish, both in oral and written forms; to be able to author and comprehend written reports, to be able to prepare design and implementation reports, to present effectively, to be able to give and receive clear and comprehensible instructions. | |||||
| 8 | To have knowledge about global and social impact of engineering practices on health, environment, and safety; to have knowledge about contemporary issues as they pertain to engineering; to be aware of the legal ramifications of engineering solutions. | |||||
| 9 | To be aware of ethical behavior, professional and ethical responsibility; information on standards used in engineering applications. | |||||
| 10 | To have knowledge about industrial practices such as project management, risk management and change management; to have awareness of entrepreneurship and innovation; to have knowledge about sustainable development. | |||||
| 11 | Using a foreign language, he collects information about Mechatronics Engineering and communicates with his colleagues. ("European Language Portfolio Global Scale", Level B1) | |||||
| 12 | To be able to use the second foreign language at intermediate level. | |||||
| 13 | To recognize the need for lifelong learning; to be able to access information; to be able to follow developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Mechatronics Engineering. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
