EMÜ679 - ADVANCED MATHEMATICAL MODELING IN OPERATIONS RESEARCH
| Course Name | Code | Semester | Theory (hours/week) |
Application (hours/week) |
Credit | ECTS |
|---|---|---|---|---|---|---|
| ADVANCED MATHEMATICAL MODELING IN OPERATIONS RESEARCH | EMÜ679 | Any Semester/Year | 3 | 0 | 3 | 10 |
| Prequisites | ||||||
| Course language | Turkish | |||||
| Course type | Elective | |||||
| Mode of Delivery | Face-to-Face | |||||
| Learning and teaching strategies | Lecture Question and Answer Problem Solving Other: Lecture, question and answer, problem solving, homeworks, individual study. | |||||
| Instructor (s) | To be determined by the department | |||||
| Course objective | The objective of this course is to introduce advanced mathematical modeling techniques; to develop students? skills to build good models for a wide variety of operations research problems, solve these models and interpret the results. | |||||
| Learning outcomes |
| |||||
| Course Content | Components and structure of mathematical programming models Modeling techniques for linear, integer and nonlinear programming problems in operations research Approaches to complex and hard-to-solve mathematical models Applications of different mathematical models from the literature | |||||
| References | Williams, HP. (2013) Model Building in Mathematical Programming, Wiley, 5th Edition. Bradley, S.P., Hax, A.C. and Magnanti, T.L. (1977) Applied Mathematical Programming, Addison-Wesley PC. Wolsey, L.A. (1998) Integer Programming, 1st ed. Wiley. Griva I., Nash S.G. and Sofer A. (2009), Linear and Nonlinear Optimization, SIAM. | |||||
Course outline weekly
| Weeks | Topics |
|---|---|
| Week 1 | Introduction to mathematical modeling, basics of Linear Programming (LP) models, assumptions, different types of objectives, variables and constraints; building a good model |
| Week 2 | Duals of LP models, primal-dual relationships, duality theorems, sensitivity analysis |
| Week 3 | Lagrangian Relaxation |
| Week 4 | Decomposition |
| Week 5 | Column Generation |
| Week 6 | Modeling of multi-objective problems, goal programming formulations |
| Week 7 | Ara sınav |
| Week 8 | Multi-period models, Stochastic Programming |
| Week 9 | Network models, Critical Path Method modeling of projects, modeling projects with resource constraints, crashing options |
| Week 10 | Integer Programming models - Combinatorial problems, problems with totally unimodular matrices |
| Week 11 | Midterm Exam |
| Week 12 | Integer Programming models - Logical conditions and 0-1 variables, disjunctive constraints |
| Week 13 | Integer Programming models ? Good and ideal formulations, valid inequalities, problem reductions |
| Week 14 | Nonlinear Programming problems, piecewise linear functions, function fitting |
| Week 15 | Study for the Final Exam |
| Week 16 | Final Exam |
Assesment methods
| Course activities | Number | Percentage |
|---|---|---|
| Attendance | 0 | 0 |
| Laboratory | 0 | 0 |
| Application | 0 | 0 |
| Field activities | 0 | 0 |
| Specific practical training | 0 | 0 |
| Assignments | 4 | 10 |
| Presentation | 0 | 0 |
| Project | 0 | 0 |
| Seminar | 0 | 0 |
| Midterms | 2 | 40 |
| Final exam | 1 | 50 |
| Total | 100 | |
| Percentage of semester activities contributing grade succes | 6 | 50 |
| Percentage of final exam contributing grade succes | 1 | 50 |
| Total | 100 | |
WORKLOAD AND ECTS CALCULATION
| Activities | Number | Duration (hour) | Total Work Load |
|---|---|---|---|
| Course Duration (x14) | 14 | 3 | 42 |
| Laboratory | 0 | 0 | 0 |
| Application | 0 | 0 | 0 |
| Specific practical training | 0 | 0 | 0 |
| Field activities | 0 | 0 | 0 |
| Study Hours Out of Class (Preliminary work, reinforcement, ect) | 12 | 6 | 72 |
| Presentation / Seminar Preparation | 0 | 0 | 0 |
| Project | 0 | 0 | 0 |
| Homework assignment | 4 | 20 | 80 |
| Midterms (Study duration) | 2 | 30 | 60 |
| Final Exam (Study duration) | 1 | 46 | 46 |
| Total Workload | 33 | 105 | 300 |
Matrix Of The Course Learning Outcomes Versus Program Outcomes
| D.9. Key Learning Outcomes | Contrubition level* | ||||
|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |
| 1. Reach the necessary knowledge and methods in engineering within the scope of advanced industrial engineering studies through scientific research and evaluate knowledge and methods and implement them. | X | ||||
| 2. Implement advanced analytical methods and modeling techniques to design processes, products and systems in an innovative and original way and improve them | X | ||||
| 3. Have the competency to plan, manage and monitor processes, products and systems. | X | ||||
| 4. Evaluate the data obtained from analysis of the processes, products and systems, complete limited or missing data through scientific methods, develop data driven solution approaches. | X | ||||
| 5. Develop original methods for the efficient integration of the scarce resources such as man, machine, and material, energy, capital and time to the systems and implement these. | X | ||||
| 6. Effectively utilize computer programming languages, computer software, information and communication technology to solve problems in the field of industrial engineering. | X | ||||
| 7. Report and present advanced studies, outcomes/results and the evaluations on the design, analysis, planning, monitoring and improvement of processes, products and systems. | X | ||||
| 8. Are aware of the professional responsibility, describe the technological, economic and environmental effects of the industrial engineering applications, work as an individual independently and as a team member having an understanding of the scientific ethical values, take responsibility and lead the team. | X | ||||
| 9. Are aware of the up-to-date engineering applications, follow the necessary literature for advanced researches, have the competency to reach knowledge in a foreign language, to quote and implement them. | X | ||||
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest