Programma

Decision making process. Introduction to Integer Linear Programming (ILP): relation between ILP and LP, equivalent formulations, relaxations, totally unimodular matrices, standard techniques for ILP modelling. ILP formulations: plant location, investment problem, sequencing problems, network optimization, transportation problems, set covering, set partitioning, set packing, crew scheduling. Exact algorithms: Branch and Bound, Cutting Planes, dynamic programming. Exact algorithms for binary and integer knapsack problems. Optimization on graphs: matching, vertex cover, max flow, independent set, Eulerian graphs and bipartite graphs. Use of an ILP commercial solver.

Testi Adottati

[1] M. FISCHETTI, "LEZIONI DI RICERCA OPERATIVA", EDIZIONI LIBRERIA PROGETTO PADOVA, ITALIA, 1995. (CAP. 2, 5, PARTE DEL 6 E DEL 7).
[2] R. AHUJA, T. MAGNANTI, J. ORLIN, "NETWORK FLOWS", PRENTICE HALL, 1993. (PG. 189-191, 473-475, 494-496)
[3] Lecture notes

Modalità Erogazione

Mostly lectures on blackboard plus some classes in the lab

Modalità Valutazione

The exam is in two parts: the written exam usually lasts 2 hours and the oral exam follows. The written exam consists of a number of exercises (typically, from 3 to 5), aimed at veryfing the level of understanding of the theoretical concepts and the students' ability to apply the techniques explained in class.