# OPERATIONS RESEARCH

Academic year 2018/2019 RICERCA OPERATIVA CT0120 (AF:230282 AR:111544) Frontal Lesson 6 Bachelor's Degree Programme MAT/09 1st Semester 3 VENEZIA
Contribution of the course to the overall degree programme goals
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) introding 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 problemm 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.
Expected learning outcomes
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.
Pre-requirements
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.
Contents
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 oft 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.
Referral texts
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/
Assessment methods
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 or 2 intermediate assignments during the period of lessons.
Teaching methods
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 and do the proposed exercises.
Teaching language
Italian
Further information