Introduction to Operational Research and its methods.
Linear programming models. Simplex method. Graph theory and optimization on networks. Applications to economics and management.
Notes for the course will be made available. As further reading we recommend:
1.V. Chvatal. Linear Programming. W.H. Freeman and Company, 1983.
2. F.S. Hillier, G.J. Lieberman. Ricerca Operativa. Mc Graw-Hill, 2010.
3. L.R. Ford, D.R. Fulkerson. Flows in Networks. Princeton University Press, 1962.
4. C. Demetrescu, I. Finocchi, G. Italiano. Algoritmi e strutture dati. Mc Graw-Hill, 2008.
Learning Objectives
Building mathematical models describing simple decision problems.
Analysing those models and compute their optimal solutions using suitable algorithms.
Prerequisites
Basic algebra of polynomials, equations and systems.
Teaching Methods
The course consists of 4 hours of lectures a week.
Further information
The course will be given by two professors: Michele Gori (Linear Programming) and Domenico Colucci (Network Theory).
Type of Assessment
Written and oral examination.
Course program
Linear Programming.
Introduction to Operations Research and its methods. Outlines on polynomial equations and inequalities. Optimization problems. Linear programs and main models (resource allocation problems, mixing problems, financing problems). Graphic methods to solve linear programs
having two decision variables. Dictionaries and outlines on linear sistems. Linear programs in standard form. Simplex method. Basic optimality conditions.
Graphs and networks.
Patterns of proof and induction. Trees, graphs and networks: introduction to the langauge and some useful results.
Algorithms, correctness, complexity and the O notation. Minimum spanning trees, shortest paths and maximum flow over a network. Applications.