| Course Name | Art of Mathematical Modelling |
| Code | Semester | Theory (hour/week) | Application/Lab (hour/week) | Local Credits | ECTS |
|---|---|---|---|---|---|
| ISE 336 | Fall/Spring | 2 | 2 | 3 | 4 |
| 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 | X |
| Major Area Courses | ||
| Supportive Courses | ||
| Media and Managment Skills Courses | ||
| Transferable Skill Courses |
| Week | Subjects | Required Materials |
| 1 | Introduction to Mathematical Modeling and OPL | |
| 2 | Building Linear Programming Models I : Workforce Planning | Homework |
| 3 | Building Linear Programming Models II: Supply planning and CPM models | Homework |
| 4 | Linearizing Logical Forms with Binary Variables, Quiz I | Homework |
| 5 | Building Integer Programming Models: Modeling integer programming models with conditional decisions, set packing, covering and partitioning problems | Homework |
| 6 | Algorithm development and programming with ILOG OPL | Homework |
| 7 | Quadratic Assignment Problem Model Formulations and Heuristic Solution Algorithms | |
| 8 | Traveling Salesman Problem Model Formulations and Heuristic Solution Algorithms, Cutting Stock Problem | Homework |
| 9 | Industrial Applications of Integer Programming I : Lot Sizing and Scheduling Models, Wagner Whitin Algorithm, Vehicle Routing Problem | Homework |
| 10 | Industrial Applications of Integer Programming II : Assembly Line Balancing , Dedicated Storage System Models and Heuristic Solution Algorithms | Homework |
| 11 | Industrial Applications of Integer Programming III : Modeling Machine Scheduling Problems I : Single Machine and Job Shop Scheduling Problems | Homework |
| 12 | Industrial Applications of Integer Programming IV : Modeling Machine Scheduling Problems II : Single Machine and Job Shop Scheduling Problems with sequence dependent setup times | Homework |
| 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 | Homework |
| 14 | Project Presentations, Quiz II | Reading journal papers |
| 15 | General Review, Discussion and Evaluation | |
| 16 | Review |
| 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 | ||
| Laboratory / Application | ||
| Field Work | ||
| Quizzes / Studio Critiques | 2 | 20 |
| Portfolio | ||
| Homework / Assignments | 12 | 20 |
| Presentation / Jury | ||
| Project | 1 | 20 |
| Seminar / Workshop | ||
| Oral Exam | ||
| Midterm | 1 | 20 |
| Final Exam | 1 | 20 |
| Total |
| Weighting of Semester Activities on the Final Grade | 80 | |
| Weighting of End-of-Semester Activities on the Final Grade | 20 | |
| 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 | 15 | 1 | 15 |
| Field Work | |||
| Quizzes / Studio Critiques | 2 | 2 | |
| Portfolio | |||
| Homework / Assignments | 12 | 1 | |
| Presentation / Jury | |||
| Project | 1 | 15 | |
| Seminar / Workshop | |||
| Oral Exam | |||
| Midterms | 1 | 6 | |
| Final Exams | 1 | 6 | |
| Total | 122 |
| # | Program Competencies/Outcomes | * Contribution Level | ||||
1 | 2 | 3 | 4 | 5 | ||
| 1 | To be able to have a grasp of basic mathematics, applied mathematics or theories and applications of statistics. | |||||
| 2 | To be able to use advanced theoretical and applied knowledge, interpret and evaluate data, define and analyze problems, develop solutions based on research and proofs by using acquired advanced knowledge and skills within the fields of mathematics or statistics. | |||||
| 3 | To be able to apply mathematics or statistics in real life phenomena with interdisciplinary approach and discover their potentials. | |||||
| 4 | To be able to evaluate the knowledge and skills acquired at an advanced level in the field with a critical approach and develop positive attitude towards lifelong learning. | X | ||||
| 5 | To be able to share the ideas and solution proposals to problems on issues in the field with professionals, non-professionals. | X | ||||
| 6 | To be able to take responsibility both as a team member or individual in order to solve unexpected complex problems faced within the implementations in the field, planning and managing activities towards the development of subordinates in the framework of a project. | |||||
| 7 | To be able to use informatics and communication technologies with at least a minimum level of European Computer Driving License Advanced Level software knowledge. | |||||
| 8 | To be able to act in accordance with social, scientific, cultural and ethical values on the stages of gathering, implementation and release of the results of data related to the field. | |||||
| 9 | To be able to possess sufficient consciousness about the issues of universality of social rights, social justice, quality, cultural values and also environmental protection, worker's health and security. | X | ||||
| 10 | To be able to connect concrete events and transfer solutions, collect data, analyze and interpret results using scientific methods and having a way of abstract thinking. | |||||
| 11 | To be able to collect data in the areas of Mathematics or Statistics and communicate with colleagues in a foreign language. | |||||
| 12 | To be able to speak a second foreign language at a medium level of fluency efficiently. | |||||
| 13 | To be able to relate the knowledge accumulated throughout the human history to their field of expertise. | |||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest
