OPERATIONS RESEARCH

This course (Operations Research - OR) represents an advanced course in the curriculum of any undergraduate student of INFORMATICA - TECNOLOGIE E SCIENZE DELL'INFORMAZIONE. Its main tasks can be summarized as follows:

(a) introducing the student to the approach problem - model - algorithm, focusing on Mathematical Programming (in particular Linear Programming), as a tool to formulate models for a wide range of application problems;

(b) developing the capability to create, analyze and solve a Mathematical Programming (Optimization) model for the problem in hand. The course starts from showing how Linear Programming represents a special case of Convex Programming.

A large number of applications detailed in previous courses can be recast using paradigms and instruments of OR.

The active involvement of students within both face-to-face and online activities of the course, including individual study, will allow to pursue the following results:

1) Knowledge and Understanding: of basic and advanced tools relative to Mathematical Programming, involving 'n' real variables;

2) Capability to Apply Knowledge and Understanding: to generate/manipulate quantitative models of Mathematical Programming, with reference to all applied sciences;

3) Capability to Judge and Interpret: using and manipulating mathematical models, on the basis of specific and analytical indicators.

The course requires a basic knowledge of Math (numbers, sequences, linear algebra, calculus with one-two unknowns) as a Prerequisite.

Students should provably know the contents of the MATHEMATICS course. In particular, students must be able to work with the following
concepts: systems of equalities and inequalities, linear algebra for matrices, extreme points of functions with one unknown, functions with
two unknowns, derivatives of functions with one unknown.
An initial test will indicate the level of knowledge expected by the students.
A final test will indicate the acquired level of knowledge by the students.

The course will cover the following topics:

1. Convex Programming and Linear Programming (LP): examples.
2. The assessment and the graphical solution of a LP. Basics on Linear algebra.
3. Basic results for Convex Programming.
4. The Fundamental Theorem in LP.
5. The Simplex method (notes). Phase I and Phase II of the Simplex method (notes).
6. Duality theory. Theorems of duality: primal and dual problem properties. Sensitivity analysis and Complementarity theorems.
7. Transportation problems.
8. Flow problems on a planar graph.
9. Fixed Cost and Mutually Exclusive constraints for Integer Linear Programming.
10. The Branch and Bound method for Mixed Integer Programming.

The next references are advised to better assimilate the contents of the course. Apart from the handouts and the exercises by the teacher, the book-reference in b) can be considered "not essential":

a) Afternotes by the teacher, available on https://moodle.unive.it/

b) L.Grippo, M.Sciandrone “Metodi di ottimizzazione non vincolata”, serie UNITEXT, Springer, 2011

c) Further materials proposed by the teacher (notes, exercises, examples, etc.), available on https://moodle.unive.it/

A written test is assigned, lasting about 1.5-2 hours. Then, based on the results of its correction, the teacher communicates the students if he/she is allowed to join the oral part of the exam, which takes place in the same day of the written part. There will be also 1 intermediate assignment during the period of lessons. The intermediate assignment will have a grade in the range 0-30 / 30, and will focus on issues in reference (a). The teacher publishes fully solved exam exercises and intermediate calls, relative to the previous academic years, on https://moodle.unive.it

For students who have passed the intermediate call with a grade >= 18, the exam in each call will include:
- Written Part with 2/3 exercises + 1/2 written questions (on the entire programme excluding the reference (a));
- (Possibly) Oral Part in case the evaluation of the written part + intermediate assignment were not sufficient.
The exercises may refer to the next arguments: Branch & Bound, Binary Knapsack, Network Flows.

For students who have NOT joined the intermediate call or have NOT passed it with a grade >= 18, the exam in each call with include:
- Written Part with 4/5 exercises + 2/3 written questions (on the entire programme);
- (Possibly) Oral Part in case the evaluation of the written part were not sufficient.
The exercises may refer to the next arguments: Convexity/Concavity, Mean value Theorems, Maxima/Minima of real functions, Models of Linear Programming or Integer Linear Programming, Vertices of polyhedra, Graphical solutions of Linear Programming problems, Branch & Bound, Binary Knapsack, Network Flows.

The grade 'X' will be given by the (arithmetic) mean with rounding of the grades reported in the intermediate call (where present) and in the written part. The Oral Part may last 20-25 minutes and will include questions on the written part and on the programme. Moreover, the oral part may contribute to increase/decrease the grade 'X' of at most 3/30.

In any case, regardless of attending or non-attending mode:
A. Scores in the range of 18-22 will be assigned when:
- Adequate knowledge and applied understanding in reference to the curriculum are demonstrated.
- Limited ability to collect and/or interpret data and formulate independent judgments.
- Sufficient communication skills, especially regarding the use of specific language related to the economic
functioning of public services.
B. Scores in the range of 23-26 will be assigned when:
- Good knowledge and applied understanding in reference to the curriculum are demonstrated.
- Fair ability to collect and/or interpret data and formulate independent judgments.
- Adequate communication skills, especially regarding the use of specific language related to the economic
functioning of public services.
C. Scores in the range of 27-30 will be assigned when:
- Good or excellent knowledge and applied understanding in reference to the curriculum are demonstrated.
- Reasonable or excellent ability to collect and/or interpret data and formulate independent judgments.
- Fully appropriate communication skills, especially regarding the use of specific language related to the
economic functioning of public services.
D. Honors will be granted when there is excellent knowledge and applied understanding in reference to the
curriculum, exceptional judgment, and communication skills.

This is a "Face-o-face" course which adopts also additional teaching materials available on the e-learning platform https://moodle.unive.it/ .
The online teaching materials report the contents of both lessons and exercises. Students are required to actively participate, practice during the face-to-face and online lessons, solve the proposed exercises, in order to pursue:
1) Knowledge and Understanding of the subject, during the interaction with the teacher;
2) Capability to Apply Knowledge and Understanding, in order to handle Mathematical Programming models in applied sciences;
3) Capability to Judge and Interpret new instances, when dealing with applications.

Italian

See also the e-learning platform https://moodle.unive.it for further info/documents/downloads.

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.

written and oral

This subject deals with topics related to the macro-area "Human capital, health, education" and contributes to the achievement of one or more goals of U. N. Agenda for Sustainable Development