Linear Programming

Code	13911
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	N.A.
Learning outcomes	i) Formulate problems using Linear Programming ii) Learn and apply fundamental concepts and results of polyhedral sets and convex analysis iii) Analyse, understand and apply the Simplex Algorithm iv) Learn and apply fundamental concepts and results of duality v) Assess the consequences of changes in a problem’s parameters (post-optimization and sensitivity analysis)
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
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.
Language	Portuguese. Tutorial support is available in English.