Academic year
2021/2022 Syllabus of previous years
Official course title
Course code
CT0120 (AF:306345 AR:172456)
On campus classes
ECTS credits
Degree level
Bachelor's Degree Programme
Educational sector code
1st Semester
Course year
Go to Moodle page
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 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 attendees.
A final test will indicate the acquired level of knowledge by the attendees.
The course will cover the following topics:


1. Convex Programming and Linear Programming (LP): examples.
2. Stating and solving graphically 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).
5. Duality theory. Theorems of duality: primal and dual problem properties. Sensitivity analysis and complementarity theorems.
6. Transportation problems.
7. Flow problems on a graph.
7. Branch and Bound method for Integer/Mixed 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 at 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, and will focus on issues in reference (a). The teacher publishes fully solved exam exercises and intermediate calls 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 exercises + 1 written question (on the entire programme excluding the reference (a))
- (Possibly) Oral Part in case the evaluation of the written part were not sufficient.
The 2 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 5/6 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 Oral Part may last 20-25 minutes and will include questions on the written part and on the programme. The final grade will be given by the mean of the grades at the intermediate call, at the written part and at the oral part.
This is a "Face-o-face" / "Blended" (depending on COVID-19 emergence) course which adopts also additional teaching material available on the e-learning platform https://moodle.unive.it/ .
The online teaching material reports 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
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
Definitive programme.
Last update of the programme: 01/06/2021