Introduction to Operational Research and its methods.
Linear programming models. Simplex method. Graph theory and optimization on networks. Algorithms of Kruskal, Dijkstra and Ford-Fulkerson. Applications to economics and management.
The notes of 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, 2006.
3. L.R. Ford, D.R. Fulkerson. Flows in Networks. Princeton University Press, 1962.
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 Daniela Bubboloni (Network Theory).
Type of Assessment
Written and oral examination.
Course program
First part.
Introduction to Operational 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.
Second part.
Basics of graph theory. Optimization problems of oriented and not oriented networks. Minimum distance, minimum spanning tree and maximum flow over a network. Kruskal, Dijkstra and Ford-Fulkerson algorithms. Description of the corresponding algorithms and their use through Java applets. Applications to economics and management.