# OPERATIONS RESEARCH

2018/2019
Official course title
RICERCA OPERATIVA
Course code
CT0120 (AF:230282 AR:111544)
Modality
On campus classes
ECTS credits
6
Degree level
Bachelor's Degree Programme
Educational sector code
MAT/09
Period
1st Semester
Course year
3
Where
VENEZIA
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 recasted using paradigms and instruments of OR.
The active involvement of students to the 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.
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 afternotes and the exercises by the teacher, the book-reference in b) can be considered "not essential":

a) Afternotes by the teacher, available at http://venus.unive.it/~fasano/ and https://moodle.unive.it/

b) F.S.Hillier, G.J.Lieberman `Ricerca Operativa', McGraw-Hill, 8^a edizione, 2005.

c) Further material proposed by the teacher (notes, exercises, examples, etc.), available on http://venus.unive.it/~fasano/ and https://moodle.unive.it/
A written test is assigned, lasting about 2-3 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 http://venus.unive.it/~fasano and 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 poliedra, 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 finaI 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 conventional face-to-face- course which adopts also additional teaching material available on http://venus.unive.it/~fasano and on the e-learning platform https://moodle.unive.it/ .
The online teaching material reports the contents of the lessons. Students are required to actively participate, practice during the lessons and do 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