| Code |
14770
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| Year |
2
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| Semester |
S1
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| ECTS Credits |
6
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
N.A.
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Learning outcomes |
Main objectives
This curricular unit aims at introducing the Operations Research methodology and its most relevant techniques that allow for problem solving capabilities in Management, Economy and Enginering contexts.
The student should be able to:
1. Identify the structure of a decision/optimization problem;
2. Build optimization models;
3. Use algorithms that allow for finding the optimal solution to those models;
4. Use the obtained information in order to enhance operations.
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Syllabus |
1. Introduction
1.1 The Linear Programming problem
1.2 Linear Programming modelling and examples
1.3 Graphical method
2. Linear Algebra, Convex Analysis and Polyhedral Sets
2.1 Vectors, matrices and systems of linear equations
2.2 Convex sets and functions
2.3 Extreme points, faces and directions of polyhedral sets
2.4 Basic feasible solutions
3. Simplex Algorithm
3.1 Optimality
3.2 Geometric motivation
3.3 Algebra of the Simplex Algorithm
3.4 Algorithmic description
3.5 Artificial basis
3.6 Degeneracy
4. Duality, Post-Optimization and Sensitivity Analysis
4.1 Formulation of the dual problem
4.2 Primal-dual relationships
4.3 Dual Simplex Algorithm
4.4 Economic interpretation
4.5 Post-optimization
4.6 Sensitivity analysis
5. The Transportation and Assignment Problems
5.1 The transportation problem
5.2 The assignment problem
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Main Bibliography |
- Bazaraa, M., Jarvis, J., Sherali, H. (2010). Linear Programming and Network Flows. Wiley.
- Hillier, F.S., Lieberman, G.J. (1990). Introduction to Operations Research. McGraw Hill.
- Ramalhete, M., Guerreiro, J., Magalhães, A. (1995). Programação Linear, Vol. I e II. McGraw-Hill.
- Tavares, L., Oliveira, R., Themido, I. e Correia, F. (1996). Investigação Operacional. McGraw-Hill.
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Teaching Methodologies and Assessment Criteria |
Two written tests, 10 points each, on the following dates:
November 9, 2023;
January 11, 2024.
Obtaining 9.5 or more points in total exempts the student from the final evaluation consisting of a written exam.
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Language |
Portuguese. Tutorial support is available in English.
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