| Area of Mathematics: | Statistics-Probability-Operational Research | ||
| Semester: | 5ο | ||
| Course ID: | 51303 | ||
| Course Type: | Compulsory | ||
| Teaching hours per week: | Theory: 3 | Practice: 2 | Laboratory: 0 |
| ECTS : | 6 | ||
| Eclass: | For the course’s material, click here. | ||
| Instructors: | Giorgos Kapetanakis και Panagiotis Papadopoulos | ||
Description
- The origins of Operational Research. The nature of Operational Research. The impact of Operational Research on the Economy.The concept of “Optimization”.Mathematical programming.Development of Mathematical Models for Solving Optimization Problems.
- The subject and history of Linear Programming (LP).Basic modeling rules.Formulation of the Linear Programming Problem (LPP). Objective function.Feasible solution.Optimal solution.
- LPP in two dimensions: Graphical method.Unique optimal solution.Infinite number of optimal solutions. Non compatible constraints.Unbounded feasible set.UnboundedRedundant constraints.
- Introduction to the Simplex Method.Basic solutions and basic feasible solutions.The basic feasible solutions corresponding to extreme points.Canonical form of an LPP.Simplex form of an LPP. Simplex tableau.Feasible value of the objective function.Optimal value theorem. Unbounded objective function theorem.Transformations of the Simplex tableau. Entering and leaving variable: Dantzig criteria.Optimality condition.Complete formulation of the Algorithm.Examples.
- Initial basis.The big M method. Examples.The two-phase method.Degenerate basic feasible solutions.Variables without sign restriction.Examples.
- Dual LPP. Economic interpretation of dual LPP. Duality Theorem. Dual Simplex Method. Examples.
- Sensitivity analysis. Examples. Introduction of a new variable. Introduction of a new constraint. Examples. Integer LP and mixed-integer LP. Examples. The assignment problem. The transportation problem. Time minimizing transportation problem.
Bibliography
- Hillier, G. Lieberman. Introduction to Operations Research, 11th Edition. McGraw Hill, 2021.
- Taha. Operations Research: An Introduction, 10th Edition. Pearson, 2017.
