Operations Research I(IND371)
| Course Code | Course Name | Semester | Theory | Practice | Lab | Credit | ECTS |
|---|---|---|---|---|---|---|---|
| IND371 | Operations Research I | 5 | 4 | 0 | 0 | 4 | 5 |
| Prerequisites | ING207 |
| Admission Requirements | ING207 |
| Language of Instruction | French |
| Course Type | Compulsory |
| Course Level | Bachelor Degree |
| Course Instructor(s) | E. Ertuğrul KARSAK ekarsak@gsu.edu.tr (Email) |
| Assistant | |
| Objective | The aim of this course is to equip students with pertinent modeling and mathematical programming knowledge and skills for solving decision making problems. |
| Content |
- Introduction - Stages of modeling - Introduction to linear programming - Graphical solution - Linear programming model - Assumptions of linear programming - Additional examples of linear programming - Simplex method - Algebra of the simplex method - Simplex method in tabular form - Artificial variables technique - Big M method - Two-phase method - Degeneracy; Alternative optimal solutions; Unbounded solution; Infeasible solution - Post-optimality analysis - Quiz I - Theory of the simplex method - Revised simplex method - Duality - Duality theory - Economic interpretation of duality - Complementary slackness theorem - Midterm - Presentation of an LP solver - Dual simplex method - Sensitivity analysis - Bounded variables technique - Transportation problem - Definition of the transportation problem - Finding an initial basic feasible solution - Transportation simplex method - Assignment problem - Quiz 2 - Network models - Terminology of networks - Shortest-path problem - Minimum spanning tree problem - Dynamic programming - Introduction - Principle of optimality - Examples of deterministic dynamic programming |
| Course Learning Outcomes |
At the end of this course, students will acquire the following skills: 1. Mathematical modeling, 2. Linear programming, 3. Transportation and assignment problems, 4. Network models, 5. Deterministic dynamic programming. |
| Teaching and Learning Methods | Lecture; problem sessions; discussion; self study. |
| References |
- Hillier, F.S., Lieberman, G.J., Introduction to Mathematical Programming, McGraw-Hill, 1995. - Bazaraa, M.S., Jarvis, J.J., Sherali, H.D., Linear Programming and Network Flows, John Wiley & Sons, 1990. - Taha, H.A., Operations Research: An Introduction, Tenth edition, Pearson, 2017. |
Theory Topics
| Week | Weekly Contents |
|---|---|
| 1 | Stages of modeling; Introduction to linear programming; Graphical solution |
| 2 | Linear programming model; Assumptions of linear programming; Additional examples of linear programming |
| 3 | Simplex method; Algebra of the simplex method; Simplex method in tabular form |
| 4 | Artificial variables technique; Big M method; Two-phase method |
| 5 | Degeneracy, alternative optima, unbounded solution, infeasible solution; Post-optimality analysis |
| 6 | Theory of the simplex method; Revised simplex method |
| 7 | Duality; Duality theory; Economic interpretation of duality; Complementary slackness theorem |
| 8 | Midterm |
| 9 | Presentation of an LP solver; Dual simplex method |
| 10 | Sensitivity analysis; Bounded variables technique |
| 11 | Transportation problem; Finding an initial basic feasible solution; Transportation simplex method |
| 12 | Assignment problem |
| 13 | Network models; Terminology of networks; Shortest-path problem; Minimum spanning tree problem |
| 14 | Dynamic programming; Principle of optimality; Examples of deterministic dynamic programming |
Practice Topics
| Week | Weekly Contents |
|---|
Contribution to Overall Grade
| Number | Contribution | |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Toplam | 4 | 100 |
In-Term Studies
| Number | Contribution | |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 30 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 20 |
| 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 | 3 | 50 |
| 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 | X | ||||
| 7 | Ability to work independently, ability to participate in working groups and have a multidisciplinary team spirit | |||||
| 8 | Ability to communicate effectively, ability to speak at least two foreign languages | |||||
| 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 | X | ||||
| 10 | Awareness of professional and ethical responsibility | |||||
| 11 | Knowledge of the concepts of professional life as "project management", "risk management" and "management of change" | X | ||||
| 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 | X | ||||
| 15 | Knowledge of the legal implications of the practice of industrial engineering | |||||
| Activities | Number | Period | Total Workload |
|---|---|---|---|
| Class Hours | 14 | 4 | 56 |
| Working Hours out of Class | 13 | 3 | 39 |
| Midterm Examinations (including preparation) | 1 | 10 | 10 |
| Final Examinations (including preparation) | 1 | 14 | 14 |
| Quiz | 2 | 9 | 18 |
| Total Workload | 137 | ||
| Total Workload / 25 | 5.48 | ||
| Credits ECTS | 5 | ||