The course aims to provide the main concepts, models and tools of Operational Research that allow to solve a wide spectrum of complex decision problems.
Knowledge and understanding
The student must demonstrate knowledge and understanding of:
a) the main aspects of optimization problems;
b) the methodologies and software tools for solving optimization problems
Applying knowledge and understanding
The student must demonstrate to be able:
a) to know a set of methods and understand their use in different contexts;
b) to formulate problems analytically;
c) to select the most suitable methods for solving the problems;
d) to use software tools to solve decision problems.
The student must be able:
a) to know how to evaluate the resolution methodologies in relation to the considered problem;
b) to implement the most suitable algorithms needed for solving the problems
The student must have the ability to explain in a simple way the main methods of linear programming and the network models .
The student must be able to:
a) elaborate, organize, summarize the acquired course contents;
b) continuously update his/her knowledge by consulting texts and publications to solve decision making problems that are typical of Management Engineering.
Basics of linear algebra.
Introduction to Operations Research (CFU 0.5 - 4 hours):
Decision problem solving, optimization and mathematical programming problems.
Continuous optimization problems (CFU 3 - 24 hours):
Main methods to solve one-dimensional and multidimensional nonlinear optimization problems (bisection method, Newton method and dichotomous research ). (2 CFU -16 hours)
Exercises in the classroom and in the computer lab (1 CFU -8 hours).
Continuous linear optimization (CFU 3 - 24 hours):
Basics of linear algebra and polyhedral geometry; formulation of linear problems; graphic representation of a linear optimization problem (1 CFU - 8 hours).
Standard simplex algorithm; sensitivity analysis and revised simplex algorithm; duality and post-optimal analysis. (1 CFU -8 hours)
Exercises in the classroom and in the computer lab. (1 CFU -8 hours)
Network models (2.5 CFU - 20 hours):
Basic definitions of graph theory; minimum cost flow model; the shortest-route problem; Dijkstra algorithm; the Critical Path Method, the Gantt diagram.
The contents of lessons include the main methodologies to solve typical optimization problems of Operations Research. Particular attention is paid to main models and algorithms that allows to address a wide range of complex decision problems. The topics covered are: the fundamental elements of linear programming; the simplex method; the graphical analysis and geometric interpretation of the simplex method; post-optimal analysis; the formulation and resolution of linear optimization problems in Matlab; the network models.
Lectures, exercises and laboratory sessions.
Hamdy A. Taha, Operations Research: An Introduction Prentice-Hall, Inc. Upper Saddle River, NJ, USA 2006
Notes and slides provided by teacher available on website:
The objective of the exam is to check the level of achievement of the objectives previously indicated.
The exam is divided into two parts:
a) a numerical test with the aim of assessing whether the student is able to apply the methodologies studied during the course. The numerical test requires to solve linear optimization problems, non linear optimization problems and network models The test must be completed in 90 minutes, and students pass the test if at least two problems are correctly solved. b) An oral test to verify the level of knowledge of the topics covered during the course. The oral test typically consists in two questions, one dealing with linear optimization methods and one dealing with the remaining arguments of course. The oral test is usually completed in 30 minutes. The final grade is the average value of the two grades achieved by the student in the numerical and oral tests.
Time table: Wednesday from 11 to 13 e Friday from 9 to 11.
Lectures are in Italian. The professor is fluent in English and he is available to interact with students in English, also during the examination.