# Analitical Models

Code: GES12555D
9 ECTS
Duration: 15 weeks/234 hours
Scientific Area: Management

Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial

#### Sustainable Development Goals #### Learning Goals

The purpose of this course is to familiarize the student with the decision making process and with the development of analytical models. It is intended that the student acquires the following knowledge:
• Learn how to formalize and solve analytically the various optimization problems;
• Learn how to formalize and solve complex linear programming problems;
• Learn how to formalize and solve sequential decision problems;
• Learn how to formalize the various types of games and be able to apply the equilibrium concepts suitable for each type of game.
This unit develops the following competencies:
• Ability to solve complex problems and to make decisions;
• Ability to build and solve analytical models;
• Ability to develop formal reasoning.

#### Contents

1. Individual decision making under uncertainty
Elements in a decision problem
Decision criteria without probabilities
Expected value and expected utility theory
Behavioral aspects in decision making
Utility extraction methods
Sequential decision making
2. Linear Programming models
Formalization and models
Linear programming  Graphical solution
The logic of the Simplex algorithm
Sensitivity analysis and dual interpretation
3. Optimization
Derivatives
The chain rule and the implicit function theorem
Optimization
Constrained optimization with equality constraints
Constrained optimization with inequality constraints
4. Decision in situations of strategic interdependence
Formalization of a game
Static games of complete information
Dynamic games of complete information
Static games of incomplete information
Dynamic games of incomplete information

#### Teaching Methods

Sessions are theoretical - practical, combining the teaching of concepts with their application to particular examples. The sessions include the resolution of practical exercises. PowerPoint presentations are used in combination with blackboard, used to show theoretical results and to solve exercises). Students must complete four group projects, where they have to put into practice their modeling skills and solve analytical problems.
In two group projects the students assume the role of a firm whose mission is to solve a particular problem. The students should use the appropriate software and have to prepare a report that includes the analysis of the problem and recommendations. The two other practical problem sets are more analytical in nature and aim to help students in developing the ability to perform formal reasoning.
The final grade is based in 4 group projects and a final exam. The final grade gives a weight of 10% to each group project and 60% to the final exam.