MATHEMATICS FOR PROJECT MANAGEMENT AND EVALUATION

The course is an introduction to the formal analysis of decision and evaluation processes, with a special attention questions that emerge in the management of cultural organizations. It is thought as a theoretical course whose pursue is to develop the quantitative tools needed for real-world applications.

The goal of the course is to develop the following abilities:
1) Reduce a programming problem to its elementary components, and find the correct instruments to analyze them;
2) Recognize when the critical aspects of a problem are due to incompatibility, sub-optimality or instability issues.
3) Discuss the main procedure for the numerical solution of programming problems, and use them in the case of linear problems.
4) Recognize and evaluate a problem in the strategic environment in which it is settled.
Special applications will address the following problems: the compatibility of groups of selection criteria, the aggregation of multiple evaluation criteria in a single one, the creation of cooperation incentives within groups, the efficient organization of resources, the adoption of conservative strategies in conflictual situations.

During the course it is assumed that students already know some mathematical subjects covered in secondary school courses. In particular it will be required some familiarity with the solution of equations, the graphical representation of elementary functions and vectors.

The program consists of a section on preliminaries and four chapters, each one addressing a specific aspect of programming problems: Feasibility, Optimality, Sensitivity and Strategic issues.
1. Preliminaries: Vectors and matrices, systems of linear equations.
2. Feasibility: Positive solutions to systems of linear inequalities; Geometric properties; Algorithmic procedures (pivoting) to determine the compatibility of a set of linear constraints.
3. Optimality: Introduction to linear programming; Geometrical characterization of optimal solutions; Graphical resolution methods; Ideas on algorithmic resolution methods.
4. Strategic issues: Introduction to Game Theory; Strategies; Strictly competitive (zero-sum) games; Conservative strategies (minimax).
We will explore applications to the problem of aggregating multiple, different evaluation criteria (Harsanyi theory of utilitarianism); creating the cooperation incentives within groups (core of TU games), alternative notions of equilibria in games.

David Vella, Invitation to Linear Programming and Game Theory, Cambridge University Press, 2021.

The final evaluation is based on a written exam with numerical and theoretical questions. At the discretion of the teacher, it may be required an oral part.

written and oral

The course consist in 15 in person classes devoted to the theoretical aspects of the subject, its applications and the resolution of exercises. Additional reading material will be provided.