﻿ Mathematical Models for Supporting Analysis and Decision-Making - Mestrado em Analítica e Inteligência OrganizacionalInstituto Politécnico de Tomar

# Analítica e Inteligência Organizacional

## Mathematical Models for Supporting Analysis and Decision-Making

Publication in the Diário da República: Despacho n.º 8956/2023 - 31/08/2023

8 ECTS; 1º Ano, Anual, 28,0 T + 28,0 TP + 4,0 S , Cód. 39325.

Lecturer
- Ricardo Jorge Viegas Covas (2)
- João Manuel Mourão Patrício (1)(2)

(1) Docente Responsável
(2) Docente que lecciona

Prerequisites
Not applicable.

Objectives
Evaluate real management and engineering problems and design strategies for modeling and solving them using advanced software, be able to interpret the information and integrate it into mathematical models for data and risk analysis.

Program
1. Operational Research (OR): basic concepts and their place in planning processes
1.1 Framework of OR in decision-making processes
1.2 Objective function, decision variables, restrictions and technological coefficients

2. Introduction to IBM/ILOG GAMS Software.

3. Modeling and solving linear programming problems.
3.1 General linear problems
3.2 Integer linear problems
3.3 Application to minimum cost flow and maximum flow problems

4 Fundamentals of Descriptive Statistics
4.1 Frequency table
4.2 Location and dispersion measures
4.3 Association measures
4.3 Crossing variables
4.4 Graphical representation of results

5 Fundamentals of Statistical Inference
5.1 Estimation theory
5.2 Decision theory
5.2.1 Probability of significance
5.2.2 Confidence intervals vs. Hypothesis testing

Statistics Multivariate Analysis

6 Multivariate Linear Regression Analysis
6.1 The type I linear regression model
6.2 The least squares method
6.3 Inference about the linear regression model
6.4 Validation of linear regression model assumptions
6.5 Variable selection (Forward, Backward and Stepwise)
6.6 Collinearity diagnostics
6.7 Response prediction
6.8 The type II linear regression model

7 Principal Component Analysis (PCA)
7.1 Introduction. applications
7.2 Factor Analysis and main components
7.3 Derivation of the main components
7.4 Decomposition of total variance
7.5 Weights and correlations between variables and main components. Eigenvalue analysis.

Evaluation Methodology
Continuous assessment consists of carrying out practical work, covering the topics covered in this Curricular Unit. A grade equal to or greater than 9.5 in this component exempts from taking the exam, which consists of a written test.

Bibliography
- Guerreiro, J. e Ramalhete, M. e Magalhães, A. (1994). Programação Linear. Lisboa: McGraw-Hill
- Magnanti, J. e Ahuja, R. (1983). Network Flows: Theory, Algorithms and Applications. New Jersey: Prentice-Hall
- Mann, P. (2001). Introductory Statistics. New York: John Wiley & Sons, Inc.
- Pedrosa, A. e Gama, M. (2004). Introdução Computacional à  Probabilidade e Estatística. Portugal: Porto Editora

Teaching Method
Theoretical-practical sessions supported by powerpoint presentations, and practical exercises.

Software used in class
GAMS/CPLEX and IBM SPSS.