The course aims at educating undergraduate students in the scientific field of Operational Research and Management Science (Decision Making) with applications in Engineering.
The objective is to familiarize students with the basic knowledge, methods, techniques and skills required to analyze, model and optimize systems and solve related problems that often involve the allocation of limited resources and competitive activities.
The course focuses on Mathematical Programming, in particular on Linear Programming and the basic principles of Integer and Mixed Integral Linear Programming. In detail:
- the graphical method and the Simplex method for solving Linear Programming problems with continuous variables
- sensitivity analysis and duality theory
- integration of integer variables in mathematical models
Course’s important goal is the use of modern software tools for a modern and integrated application of theory in Engineering discipline.
After completing the course, students will be able to:
- Understand the importance of Decision Making, its process, conditions and stakeholders.
- Identify and associate real problems with standard Operational Research problems.
- Build standard Mathematical Programming models.
- Select the most appropriate method for solving optimization problems.
- Understand and interpret the solution results and identify the most important parameters of the problem.
- Assess the impact of resulting solutions under a comprehensive and multidimensional perspective.
- Use information technology tools to build and solve optimization problems as also performing solution analysis.
Search for, analysis and synthesis of data and information, using the necessary technology
Formulation, Modeling and Problem Solving
Learning to use software tools
Working in an interdisciplinary environment
Production of free, creative and inductive thinking
There are typically no prerequisite courses. Only need basic knowledge in Mathematics and Informatics.
Section 1: Decision Science, Introduction, Concepts. Structural elements of a decision-making problem. Conditions & Actors in Decision Making. Business Decision Making Process.
Section 2: Operational Research, Introduction, Historical Background. Operational Research Problems. Process and methodology of problem solving. Applications in Engineering.
Section 3: Mathematical Programming. Linear Programming, Introduction, Concepts. Linear Programming problem configuration and structural elements. Mathematical modeling of problems. Common modeling errors in Linear Programming. Handling nonlinear mathematical relationships.
Section 4: Graphic solution of Linear Programming problems. Algebraic calculation of endpoint solutions. Slack variables. Revised Linear Programming problem. Multiple optimal solutions, Infeasible solutions. Learning software tools and performing exercises (Microsoft Excel)
Section 5: Simplex method. Symbols, Definitions. Simplex algorithm. Solving Linear Programming problems. Interpretation of Simplex Tableau. Learning software tools and performing exercises (Solver @ Microsoft Excel, LINDO).
Section 6: Sensitivity analysis, Changes in objective function coefficients, Changes in constant terms of constraints. Duality theory. Dual prices, Shadow prices. Primary-Dual problem relationships. Learning software tools and performing exercises (Solver @ Microsoft Excel, LINDO).
Section 7: Linear Programming examples applied in Engineering and Industry. The transportation problem. Learning software tools and performing exercises (Solver @ Microsoft Excel, LINDO, GAMS).
Section 8: Minimization problems. Problems with >= constraints. Artificial variables. Big M Method. Adaptive use of Simplex method.
Section 9: Integer Linear Programming, Concepts, Purpose, Configuration and structural elements of Integer and Mixed Integer Linear Programming problems. Binary Variables. Problems mathematical modeling. Presentation of Integral Programming problems.
Microsoft PowerPoint Slides
Exercises and problems solving with software tools (Microsoft Excel, Solver @ Microsoft Excel, LINDO, GAMS)
Educational process support through e-class
Study & Analysis of Literature
Total Module Workload (ECTS Standards):
The language of evaluation is Greek.
The evaluation includes: Written examination (100% of the final mark)
The evaluation criteria are explicitly mentioned in the course’s eClass (in Greek): E-Class (MECH1280) [link: https://eclass.upatras.gr/courses/MECH1280/] and in course sheet in Departmental Curriculum.
1. Hamdy A. Taha, “Operations Research”, 10th Edition, Tziola Publications, 2017 [Book Code in Eudoxus: 59415056]
2. Frederick S. Hillier, Gerald J. Lieberman, Alexandros Diamantidis (ed.), “Introduction To Operations Research», Tziola Publications, 2007 [Book Code in Eudoxus: 59386820]
3. Pantelis Ipsilantis, “Operational research. Methods and techniques of decision making”, 5th Edition, Propobos Publications, 2015 [Book Code in Eudoxus: 50659326]
4. Anderson David R., Sweeney Dennis J., Williams Thomas A., Martin Kipp, “Management Science”, Kritiki Publishing, 2014 [Book Code in Eudoxus: 41955482]
5. Michael J. Panik, “Linear Programming and Resource Allocation Modeling”, Wiley, 2018 [Book Code in Eudoxus: 91719943]