| 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 | X | |
| 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 adequate knowledge in Mathematics, Science and Industrial Engineering; to be able to use theoretical and applied information in these areas to model and solve Industrial Engineering problems. | X | ||||
| 2 | To be able to identify, formulate and solve complex Industrial Engineering problems by using state-of-the-art methods, techniques and equipment; to be able to select and apply proper analysis and modeling methods for this purpose. | X | ||||
| 3 | To be able to analyze a complex system, process, device or product, and to design with realistic limitations to meet the requirements using modern design techniques. | X | ||||
| 4 | To be able to choose and use the required modern techniques and tools for Industrial Engineering applications; to be able to use information technologies efficiently. | X | ||||
| 5 | To be able to design and do simulation and/or experiment, collect and analyze data and interpret the results for investigating Industrial Engineering problems and Industrial Engineering related research areas. | X | ||||
| 6 | To be able to work efficiently in Industrial Engineering disciplinary and multidisciplinary teams; to be able to work individually. | X | ||||
| 7 | To be able to communicate effectively in Turkish, both orally and in writing; 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 contemporary issues and the global and societal effects of Industrial Engineering practices on health, environment, and safety; to be aware of the legal consequences of Industrial Engineering solutions. | |||||
| 9 | To be aware of professional and ethical responsibility; to have knowledge of the standards used in Industrial Engineering practice. | |||||
| 10 | To have knowledge about business life practices such as project management, risk management, and change management; to be aware of entrepreneurship and innovation; to have knowledge about sustainable development. | |||||
| 11 | To be able to collect data in the area of Industrial Engineering; to be able to communicate with colleagues in a foreign language. | |||||
| 12 | To be able to speak a second foreign at a medium level of fluency efficiently. | |||||
| 13 | To recognize the need for lifelong learning; to be able to access information, to be able to stay current with developments in science and technology; to be able to relate the knowledge accumulated throughout the human history to Industrial Engineering. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
