ELEMENTI DI STATISTICA E GESTIONE DATI To introduce students to Statistics, both descriptive and inferential. Knowledge and understanding: understand the fundamental principles of Probability, Statistics as a tool for solving real problems ; understand in which way methods are developed and in which way they are analyzed. Applying knowledge and understanding: be able to apply methods to real problems along with implementations in some programming language. Making judgements: be able to recognize the strengths and weaknesses of the methods. Communication: know how to expose the resolution of a problem by using a suitable procedure. Lifelong learning skills: know how to gather information from the web or textbooks in order to solve problems posed in real-life situations. RICERCA OPERATIVA Knowledge and understanding: capability of understanding (a) the conceptual approach of Operations Research as a tool for formulating, solving and evaluating decision-making problems related to complex systems, (b) the methodologies for the formalization of quantitative models and algorithmic solutions, and (c) the theoretical aspects underlying the solution techniques, their mathematical justifications and their implications and applicative potentialities. Applying knowledge and understanding: capability of actually applying the solution techniques and algorithms, by executing the necessary procedures to attain the solution of numerical problems and being able to critically analyze the solutions obtained. Making judgments: capability of applying the acquired knowledge to autonomously formulate quantitative models and solve the associated optimization problems, by also manually executing the appropriate solution algorithms. Communication skills: capability of introducing decision-making problems and their possible solutions, both in written and oral form, and to critically discuss the validity and the limits of formulations and solutions. Learning skills: capability of gathering information from textbooks, scientific papers and other material for the formulation and autonomous solution of decision-making problems.

Basics of calculus and linear algebra.

ELEMENTI DI STATISTICA E GESTIONE DATI Descriptive Statistics, Probability, discrete random variables, continuous random variables, inferential Statistics: sampling statistics, estimation, testing Statistical Hypotheses. RICERCA OPERATIVA 1. Introduction to Operations Research Decision-making problems: Analysing and solving complex problems in order to optimise solutions. Areas of application:Business management, resource planning and management, production, logistics and transport, economics, finance, health services, public administration. 2. Linear Programming (LP) Properties and characteristics: Optimisation of a linear objective function with linear constraints. Model formulation: Decision variables, objective, constraints. Geometric interpretation: Representation in two dimensions. Possible outcomes: Feasibility, unconstrained, single or multiple optimality. Algebraic formulation: Standard form with slack and surplus variables. Simlex method: Basic solution, in-base and out-of-base variables, optimality criterion, improvement. 3. Duality in LP Dual variables and dual constraints: Correspondence between variables and constraints of primal and dual problems. Dual objective: Objective function of the dual problem. Duality theorems: Weak and strong duality, complementary slackness theorem. 4. Postoptimality Sensitivity analysis: Impact of parameter variations on optimal results, variation of right-hand side terms and coefficients of the objective. 5. Integer programming Graphical examples: Problems with integer variables. Branch & bound algorithm: Systematic exploration of solutions. Gomory cuts: Techniques for improving solutions.

ELEMENTI DI STATISTICA E GESTIONE DATI 1) Lecture notes. 2) Sheldon Ross. Introductory Statistics, Third Edition, Elsevier. RICERCA OPERATIVA F. S. Hillier and G. J. Liebermann: Ricerca Operativa, 9th Ed. McGraw-Hill

ELEMENTI DI STATISTICA E GESTIONE DATI. Introduction: the collection of data; the description of the data; drawing conclusion from the data; population and samples. Descriptive statistics, describing the data: frequency tables; pie charts; grouped data values and histograms; stem-and-leaf plots; paried data. Descriptive statistics, summarizing the data: mean; median; percentiles; mode; variance; standard deviation; interquartile range; box-plot; normal data; correlation coefficient; causation and association. Probability: experiment; sample space; events; measure of probability; probability for experiments with discrete sample space; probability for experiments with continuous sample space; conditional probability; independence of events; the Bernoulli process. Discrete random variables: discrete random variables; probability mass functions; binomial random variables; indipendence of random variables; mean of a random variable; variance of a random variable; mean and variance of a binomial random variable. Continuous random variable: continuous random variables, probability density functions; normal random variables; independence; mean and variance for Continuous random Variables; finding probabilities for normal random variables; properties of normal random variables; percentiles. Sampling Statistics: the sample mean; the central limit theorem; sampling proportions; the sample variance. Estimation: estimating the mean; estimating the mean when the standard deviation is unknown. Testing Statistical Hypotheses: statistical hypothesis; tests for normal distributions with known variance; tests for normal distributions with unknown variance. RICERCA OPERATIVA 1. Introduction to Operations Research Decision-making problems: Operations research focuses on analysing and solving complex decision-making problems, using mathematical models and algorithms to optimise solutions. 2. Linear Programming (LP) Properties, characteristics and applicability of LP Formulation of a LP model in terms of Decision variables, Objective, Constraints Geometric interpretation in two dimensions Possible outcomes of a LP problem: Feasible, Unconstrained, Single and multiple optimality. Algebraic formulation of LP: Simplex method 3. Duality in LP Dual variables and dual constraints: Each variable in the primal problem corresponds to a constraint in the dual problem and vice versa. Dual objective: The objective function of the dual problem. Duality theorems: - Weak duality: The solution of the dual problem provides an upper or lower bound to the solution of the primary problem. - Strong duality: The optimal solutions of the primal and the dual problem are equivalent. - Complementary Slackness Theorem: Relationship between the optimal primal and dual solutions. 4. Post-optimality Post-optimality and sensitivity analysis: Study of the impact of parameter variations on optimal results. Variation in right-hand side terms: Changes in the terms of the constraints. Variation in the coefficients of the objective function: Changes in the function to be optimised. 5. Integer programming Examples and graphical illustration: Problems in which the decision variables must take integer values. Branch & bound algorithm: Method for solving integer programming problems by systematically exploring possible solutions. Gomory cuts: Techniques for improving integer programming solutions.

Lectures on theory topics at the blackboard and/or with the aid of slides projected in the classroom. Exercises on theory topics either by means of examples on the blackboard or using the computer (MATLAB, Excel solver).

Students may be requested to bring their own laptop. Teaching materials are available on http://moodle2.units.it and Teams

The final mark is the average (rounded up) of the marks obtained by the student in each individual module. The grade obtained in one module does not expire for the purposes of averaging with the grade obtained in the other module. ELEMENTI DI STATISTICA E GESTIONe DEI DATI The exam consists in a written part with three exercises and, after a positive evaluation of this part, a second oral part. RICERCA OPERATIVA The final examination consists of a written test involving the completion of five exercises and, where appropriate, the answering of theory questions. It tests both the students’ knowledge of the topics covered during the course and their ability to understand and judge independently. The exercises include - Formulating (and possibly solving) a continuous linear programming model (syllabus item 1) - Graphical solution of a continuous linear programming problem (syllabus item 2) - Simplex algorithm (syllabus item 2) - Duality, Complementarity, Sensitivity (syllabus items 3 and 4) - Integer programming (syllabus item 5) The maximum score for each individual exercise varies from 4 to 8 depending on the difficulty. The total score (sum of the individual scores) is always 32. The examination is considered passed by those who obtain a score greater than or equal to 18. Those who obtain a score above 30 (i.e. 31 or 32) are awarded the grade of '30 cum laude'. Should the student be required to produce content (of any kind) in order to be admitted or to participate in an examination (projects, reports, exercises, tests), any use of Large Language Model tools (ChatGPT and the like) must be explicitly stated. This requirement must also be complied with in the case of partial use. Regardless of the assessment method used, the lecturer reserves the right to evaluate the student's actual contribution to each type of content produced through an oral examination.

This course explores topics closely related to one or more goals of the United Nations 2030 Agenda for Sustainable Development (SDGs).