# Operations Research

```. – Operations Research
PROFESSOR FRANCESCA MAGGIONI
COURSE AIMS
Operations research provides analytical tools for developing decision support
models.
Operations research tools provide a scientific approach to solving known concrete
problems in economics, logistics, industrial production and technology.
The course aims to teach the main operations research methods for solving
decision problems: linear and integer optimization, problems on graphs, project
management, dynamic programming and applications.
The course also aims to provide knowledge of the main software tools for solving
optimization models: Excel solver and the mathematical programming languages
AMPL and GAMS.
COURSE CONTENT
Prerequisites: Basic knowledge of linear algebra and use of the computer.
Specific operations research topics:
 Introduction to operations research.
 Linear programming (LP).
o Formulation of LP problems and applications.
o LP geometry: polytopes, vertices and basic solutions.
o Simplex algorithm and revised simplex algorithm.
o Duality theory and sensitivity analysis in LP.
 Integer optimization.
o Cutting-plane method (Gomory).
o Search trees and branch-and-bound algorithms.
o Knapsack problem and solution algorithms.
o Assignment and transportation problems.
 Graph optimization.
o Definitions and properties of directed and undirected graphs.
o Minimum spanning trees.
o Shortest path problems, maximum flow problems and solution
algorithms.
o Other problems on graphs (TSP and VRP).
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Project optimization.
o Directed graph representation.
o Critical path research and analysis (CPM).
Dynamic optimization.
Computational complexity of algorithms.
Overview of stochastic programming.
Textbook used:
S. MARTELLO, Ricerca operativa per la laurea magistrale, Societ&agrave; Editrice Esculapio, ISBN:
9788874884537
TEACHING METHOD
Lectures and lecture room discussions on in-depth study material provided by the
lecturer. Some lessons will take place in the computer laboratory.
ASSESSMENT METHOD
Oral examination. Presentation of a paper on topics chosen by the student. Teacher's
questions on topics related to the entire syllabus.
NOTES
Further information can be found on the lecturer's webpage
http://www2.unicatt.it/unicattolica/docenti/index.html or on the Faculty notice board.
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