MODELS AND METHODS FOR DECISION MAKING

This course belongs to the educational activities chosen by the student of the bachlor course called "Economia Aziendale". In line with the educational objectives of the degree course, this course intends to present some methods and models for business decisions with a view to learning how to perform an adequate analysis and interpretation of company facts. In particular, the course aims to deepen some fundamental concepts related to static optimization with particular reference to linear programming and multi-objective and multi-attribute programming (moodle.unive.it/course/view.php?id=1015). The course is entirely online.

Knowledge and understanding skills.
Through the study of theoretical tools, at the end of the course the student will be able to face specific problems by formulating models capable of representing these problems. In particular, the student must learn to:
- acquire the analytical and conceptual tools necessary to examine and solve management problems.

Ability to apply knowledge and understanding.
Through the deepening of the theory and the exercises the student will acquire the ability to:
- contextualize their knowledge and apply them to concrete situations;
- face new complex problems of a business nature;
- know how to choose, among the quantitative techniques seen, the most adequate to deal with the concrete problems under analysis.

Judgment skills, communication skills, learning skills.
The student, through the autonomy and the comparison with the teacher and the other students, will know:
- finding justifications for the approach used, taking into account strengths and weaknesses;
- extending what has been learned to other similar situations.

Having achieved the objectives of MATHEMATICS - 1 and MATHEMATICS – 2. In particular, the student should be able to apply his knowledge about the concepts and methods related to systems of linear equations and inequalities, matrix algebra, maximum and minimum of functions.

The course, organized in 6 teaching units, is divided into two parts.

Part 1 (4 teaching units): Linear Programming.

Teaching Unit 1:
Linear programming (PL) is introduced in the context of mathematical programming and optimization theory in general, and some important theoretical results concerning the existence and uniqueness of an optimal solution are presented.
It highlights the importance of PL presenting 3 classic problems and linear programming models (production plan of maximum profit, transport, diet).

Teaching Unit 2:
Some reference formulations of a problem PL (standard form and canonical form) are presented and the equivalence between these and all possible variants is demonstrated.
The graphic resolution of a particular PL problem (a problem of bicycle production) is discussed.
The important concept of a basic solution is introduced.

Teaching Unit 3:
The fundamental theorem of linear programming and its geometric interpretation is enunciated and demonstrated, underlining the importance of the basic solutions introduced in the previous unit, and presenting other theoretical results deriving from the previous ones and very important also from the practical point of view.
We learn to solve some linear programming problems in two variables, underlining the importance of the graphic approach, and we introduce the important concept of duality.

Teaching Unit 4:
The importance of duality is emphasized, enunciating some theorems on duality among which the conditions of complementarity that link the optimal solution of the dual problem to the optimal solution of the primal problem, provided that these solutions exist.
The method to solve couples of primary / dual PL problems is presented.
A model for the division of the advertising budget (a simple example of the usefulness of PL in concrete problems) is presented.


Part 2 (2 teaching units):

Teaching Unit 5:
Multi-objective programming is introduced, based on the premise that in many situations it is difficult to recognize a single objective in the definition of a model.
We talk about multi-criteria programming, learning to tackle two-objective PL models and introducing the concepts of efficient frontier, Pareto-optimal solutions and scalarization.
We talk about multi-attribute programming, devoting space to simple methods such as the dominance method, the maxmin and maxmax, and attribute weights, introducing the concept of coherence of the matrix of pairwise comparisons between attributes and the eigenvalue method.

Teaching Unit 6:
Some multi-attribute programming methods (conjunctive / disjunctive method, permutation method, linear assignment method) are presented.
A richer method is analyzed both from the theoretical point of view and from the application point of view, namely the AHP, providing some theoretical results and showing an applicative example.

Luenberger D. G., Ye Y. (2008), Linear and nonlinear programming, Springer.
Mason F. (1992), Metodi quantitativi per le decisioni, Giappichelli.
Mason F. (2008), Appunti di Programmazione a più criteri, Quaderni di didattica n. 29/2008, Università Ca' Foscari di Venezia.
Other teaching material prepared by the theacher will be made available on the Moodle platform of the course.

Evaluation is based on a final oral exam; admission to the final exam is possible only after completing some mandatory online activities.

Online activities.
Quiz (mandatory activity): multi choice quiz (10 questions each) will be made available weekly on the Moodle platform; they are intended to verify the acquisition of the contents related to the online activities.
Exercises (optional activities): sets of exercises will be proposed on Moodle to self-evaluation of the activities of the material carried out during the course.

Oral examination.
The oral exam includes two questions:
- the first, of a theoretical nature, which aims to verify the theoretical knowledge acquired;
- the second, an exercise, which aims to verify the ability to use the theoretical results learned during the course.

The exam is assessed on a 30-point basis. The first part, the online activity, does not give marks but allows, if passed, to access the oral exam. The oral examination, the second part, is considered passed if both the questions will have an answer assessed as sufficient.

The course "Modelli e metodi per le decisioni" is delivered entirely online, organized in 6 teaching units (weeks).
For each week there are:
- about 60 minutes of weekly videos (divided into 3 or 4 slots),
- a weekly meeting with the teacher (to be planned),
- some exercises carried out and to be carried out,
- 10 quizzes (70% of which must be done in order to be admitted to the oral exam).
To access the course you need to register on the site moodle.unive.it/course/view.php?id=1015.

Italian

The course "Modelli e metodi per le decisioni" (moodle.unive.it/course/view.php?id=1015) can be freely followed by both students of Ca 'Foscari and other students or interested persons (registration is mandatory on moodle.unive.it/course/view.php?id=1015).
Everyone must participate regularly in online activities, scheduled over 6 weeks, contribute to the forum and respond to at least 70% of the final quizzes to be admitted to the final exam.
Anyone who, in compliance with the registration with Ca 'Foscari, wishes to take the exam and receive the relative credits must take part in the oral examination in the presence.

Accessibility, Disability and Inclusion
Accommodation and support services for students with disabilities and students with specific learning impairments

Ca’ Foscari abides by Italian Law (Law 17/1999; Law 170/2010) regarding support
services and accommodation available to students with disabilities. This includes students with
mobility, visual, hearing and other disabilities (Law 17/1999), and specific learning impairments (Law 170/2010). If you have a disability or impairment that requires accommodations (i.e., alternate testing, readers, note takers or interpreters) please contact the Disability and Accessibility Offices in Student Services: disabilita@unive.it.

oral