MATHEMATICS FOR PROJECT MANAGEMENT AND EVALUATION

The course aims to provide some tools that will allow you to become familiar with quantitative methods and their use in decision-making issues, including those related to cultural organisations. The course adopts an approach oriented not only to the description of theoretical aspects but also to the applications for practical cases.

The course allows students to acquire knowledge of quantitative methodologies and to apply these concepts to formulate and solve some decision problems under certainty, uncertainty and risk, together with multicriteria problems and financial project evaluation and simple optimization problems. First lessons will be devoted to the introduction to Decision Making and pre-requirements. like elements of Linear Algebra and calculus.
Knowledge and understanding: understanding the meaning of the concept of Decision Making (DM); understanding and knowledge of methodologies capable of dealing with Decision Making problems.. Qualitative description of DM and some model about. Introduction to Multi Criteria problems (normalization, aggregation), and some MCDA methods. Knowledge and understanding of multi-objective problems and elements of discrete optimization
Application of knowledge and understanding: be able to solve decision-making problems that may also affect cultural organisations; be able to formulate and solve some decision making problems.

During the course it is assumed that students already know some mathematical subjects covered in secondary school courses, in particular the knowledge of elementary functions, properties their graphic representation; derivatives and optimization; knowledge of vectors and matrices

1. Introduction to Decision Making (DM). Decision under certainty, uncertainty, risk.

2. Linear algebra; vector and matrices. Inverse matrix, eigenvalues and eigenvectors.

3. Simple economic models and optimization.

4. Multicriteria analysis. The AHP methodology.

5. Multi objective decision making; elements of linear programming. Application to Data Envelopment Analysis (DEA).

6. Financial decision making: elements of Cost-Benefit Analysis (CBA)

7. Decision under uncertainty: EV, Maximin, Maximax, OWA, and other; decision under risk: EU, SEU.

Other optional arguments be eventually considered, like elements of Graph Theory, Decision Trees





7. Elements of Graph Theory.

Other optional arguments will be eventually considered,

Slides and other material from the Teacher will be furnished during the lessons

OTHER MATERIAL (for consultation):

Dowling Edward T., Introduction to Mathematica Economics, SCHAUM's OuTline, third edition, 2001 (free on line).

Cournejols G., Trick M., Quantitative Methods for the Management Sciences, Course Notes, Carnagie Mellon, Pittsburgh, 1999.

Forman E.H., Selly M.A., Decision by objectives (How to convince others that you are right)", World Scientific, 2001.

Decision Making, Giacomo Bonanno, http://faculty.econ.ucdavis.edu/faculty/bonanno/DM_Book.html (open access book)

The preparation is checked by means of a written proof, including exercises and description/discussion of some of the arguments introduced. Oral test will be optional.

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The course is divided into 30 hours of frontal lessons in which theoretical concepts regarding the methodologies covered by the course are presented, as well as concrete applications to decision-making problems.

Detailed information on the program and study materials will be communicated at the beginning of the course on e-learning page (www.moodle.unive.it).