. – 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). Project optimization. o Directed graph representation. o Critical path research and analysis (CPM). Dynamic optimization. Computational complexity of algorithms. Overview of stochastic programming. READING LIST Textbook used: S. MARTELLO, Ricerca operativa per la laurea magistrale, Società 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. at

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# Operations Research