Operations Research I
ekarsak@gsu.edu.tr
nagoker@gsu.edu.tr
nagoker@gsu.edu.tr
Content
Objective
The aim of this course is to equip students with pertinent modeling and mathematical programming knowledge and skills for solving decision making problems.
Course 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, Sixth edition, Prentice-Hall, 1997.
Weekly Contents
| 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 |
Assessment System
| Activities | Number | Contribution |
|---|---|---|
| Contribution of in-term studies to overall grade | 3 | 50 |
| Contribution of final exam to overall grade | 1 | 50 |
| Total | 4 | 100 |
| Activities | Number | Contribution |
|---|---|---|
| Assignments | 0 | 0 |
| Presentation | 0 | 0 |
| Midterm Examinations (including preparation) | 1 | 20 |
| Project | 0 | 0 |
| Laboratory | 0 | 0 |
| Other Applications | 0 | 0 |
| Quiz | 2 | 30 |
| 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 |
| Total | 3 | 50 |
Relation of Proficiency
| 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 | |||||
ECTS
| 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 | ||