The course aims to introduce and test some of the mathematical tools widely used in modeling and decision support systems, with particular attention to optimization and business intelligence techniques.

The course develops a first institutional part on the classical contents of operational research and a second part, with seminar methods in the classroom, on thematic topics.
To take into account the possible impossibility of students to attend, the program is divided into non-attending students and students who regularly attend lectures and seminars.

Program for non-attending students

Part A. Methods and Applications of Linear Optimization
A.1) Linear optimization
- Typical applications of linear optimization
- Formulations of linear optimization problems
A.2) Geometry of linear optimization
- Two-dimensional representations of linear optimization problems (constraints, objectives, feasible set)
- Optimal solutions and Kuhn-Tucker conditions
- Polyhedra, vertices and basic solutions
- Outline of the simplex algorithm
A.3) Duality and sensitivity analysis in linear optimization
- Examples of dual problems and duality theorems
- Sensitivity analysis with respect to the objective function and to the constraints
- Meaning of dual variables and shadow prices

Part B. Whole and graph optimization
B.1) Whole optimization
- Knapsack and Capital budgeting
- Assignment and transportation
- Cutting plan method (Gomory)
- Research trees and Branch and Bound Algorithms
B.2) Graphs and Optimization on graphs
- Definitions and properties of oriented and non-oriented graphs
- Spanning trees at minimum cost
- Minimum walking problems
- Simple network flows and with gains on the arcs
- Other graph problems (TSP, VRP)
B.3) Optimization of Projects
- Representation through oriented graphs
- Activities on knots and / or arches
- Research and Analysis of the critical path
- Probabilistic model and PERT
- Time / Cost balancing

Part C. Mathematical models and decision systems
C.1) Components of the decision-making process
- Business Intelligence
- Decision support systems
- Outline of Data Warehousing and Data Mining
C.2) Mathematical models and methods
- Mathematical models for decisions
- Data preparation and exploration
- Classification and Clustering
C.3) Applications
- Models for logistics and production
- Data Envelopment Analysis

Program for attending students

Part A. Elements of the use of MATLAB and its main programming structures
- Illustration of MATLAB and its use from the command window
- Operations with arrays and matrices
- Main programming structures
- Function in MATLAB and writing of .m files
- Examples of functions inside MATLAB

Part B. Methods and Applications of Linear Optimization
B.1) Linear optimization
- Typical applications of linear optimization
- Formulations of linear optimization problems
- Two-dimensional representations of linear optimization problems (constraints, objectives, feasible set)
- Optimal solutions and Kuhn-Tucker conditions
- Polyhedra, vertices and basic solutions
- Outline of the simplex algorithm
B.2) Duality and sensitivity analysis in linear optimization
- Examples of dual problems and duality theorems
- Sensitivity analysis with respect to the objective function and to the constraints
- Meaning of dual variables and shadow prices
B.3) MATLAB functions for linear optimization

Part C. Whole and graph optimization
C.1) Whole optimization
- Knapsack and Capital budgeting
- Assignment and transportation
- Cutting plan method (Gomory)
- Research trees and Branch and Bound Algorithms
C.2) Graphs and Optimization on graphs
- Definitions and properties of oriented and non-oriented graphs
- Spanning trees at minimum cost
- Minimum walking problems
- Simple network flows and with gains on the arcs
- Other graph problems (TSP, VRP)

Part D. Seminarial Part
Each student must participate in (at least) two of the following seminars, of his choice.
D.1) Seminar on Project Optimization
- Representation through oriented graphs
- Activities on knots and / or arches
- Research and Analysis of the critical path
- Probabilistic model and PERT
- Time / Cost balancing
D.2) Seminar on Classification and Clustering
- Classical classification
- "fuzzy" classification
D.3) Seminar on Models for Logistics and Supply Chain
- Mathematical models for logistics and distribution management
- Analysis of the agility of a logistic network
D.4) Seminar on Business Intelligence and Soft Computing Models
- Fuzzy sets and numbers
- Fuzzy logic and soft computing models

The material relating to lectures and seminars will be distributed by the teacher directly to the attending students.

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

Teaching

The institutional part is carried out through classroom lectures.
The seminar part is held in the classroom, with individual work or in small groups, with the guidance of the teacher.

Course books

1. L. Bellenzier, R. Grassi, S. Stefani, A. Torriero, Metodi Quantitativi per il Management, Esculapio Publishing Company, Bologna, 2012. All text.

1a. (alternative to 1.) Carlo Vercellis, " Ottimizzazione: teoria, metodi applicazioni", McGraw Hill, 2008. Chapters 1, 2, 3, 5, 6, 8, 9, 10.

2. Material distributed by the teacher and available on the University's Blended Learning platform.
2a. (for further information) Carlo Vercellis, "Business Intelligence: modelli matematici e sistemi per le decisioni", McGraw Hill, 2006.
Chapters 1, 2, 3 (reading), 4, 5 (reading), 6, 7, 10 (up to and including 10.3), 12 (reading), 14, 15.

Assessment

It consists of a question / interview on the topics of the program.

The acquisition of essential terminology and mathematical formalism is required, as contained in the manuals suggested for the study.

Disabilità e DSA

Le studentesse e gli studenti che hanno registrato la certificazione di disabilità o la certificazione di DSA presso l'Ufficio Inclusione e diritto allo studio, possono chiedere di utilizzare le mappe concettuali (per parole chiave) durante la prova di esame.

A tal fine, è necessario inviare le mappe, due settimane prima dell’appello di esame, alla o al docente del corso, che ne verificherà la coerenza con le indicazioni delle linee guida di ateneo e potrà chiederne la modifica.