\contentsline {section}{\numberline {1}Modelli}{3}{section.1}%
\contentsline {subsection}{\numberline {1.1}Cenni di Base}{3}{subsection.1.1}%
\contentsline {subsection}{\numberline {1.2}Esercizi}{5}{subsection.1.2}%
\contentsline {subsubsection}{\numberline {1.2.1}Problema con Delta}{5}{subsubsection.1.2.1}%
\contentsline {subsubsection}{\numberline {1.2.2}Problema con massima distanza}{6}{subsubsection.1.2.2}%
\contentsline {subsubsection}{\numberline {1.2.3}Problema Variabile Triplo indice}{7}{subsubsection.1.2.3}%
\contentsline {subsubsection}{\numberline {1.2.4}Problema di Trasporto}{9}{subsubsection.1.2.4}%
\contentsline {subsubsection}{\numberline {1.2.5}Problema di Stoccaggio}{11}{subsubsection.1.2.5}%
\contentsline {subsubsection}{\numberline {1.2.6}Problema di Stoccaggio 2}{12}{subsubsection.1.2.6}%
\contentsline {section}{\numberline {2}Forme: Standard, Canonica, Generale}{13}{section.2}%
\contentsline {subsection}{\numberline {2.1}Standard $\Rightarrow $ Canonica}{13}{subsection.2.1}%
\contentsline {subsection}{\numberline {2.2}Generale $\Rightarrow $ Standard}{13}{subsection.2.2}%
\contentsline {subsection}{\numberline {2.3}Esercizio Trasformazione Gran Fritto Misto}{14}{subsection.2.3}%
\contentsline {section}{\numberline {3}Matrici : LP, ILP}{15}{section.3}%
\contentsline {subsection}{\numberline {3.1}Fondamenti Concettuali}{15}{subsection.3.1}%
\contentsline {subsubsection}{\numberline {3.1.1}Quale Simplesso?}{15}{subsubsection.3.1.1}%
\contentsline {subsection}{\numberline {3.2}LP}{15}{subsection.3.2}%
\contentsline {subsubsection}{\numberline {3.2.1}Simplesso}{15}{subsubsection.3.2.1}%
\contentsline {subsubsection}{\numberline {3.2.2}Simplesso Duale}{16}{subsubsection.3.2.2}%
\contentsline {subsubsection}{\numberline {3.2.3}2Fasi}{17}{subsubsection.3.2.3}%
\contentsline {subsubsection}{\numberline {3.2.4}Duale del problema}{19}{subsubsection.3.2.4}%
\contentsline {subsection}{\numberline {3.3}Rappresentazione Grafica}{21}{subsection.3.3}%
\contentsline {subsection}{\numberline {3.4}ILP}{22}{subsection.3.4}%
\contentsline {subsubsection}{\numberline {3.4.1}Tagli di Gomory}{22}{subsubsection.3.4.1}%
\contentsline {subsection}{\numberline {3.5}Esercizi Particolari}{25}{subsection.3.5}%
\contentsline {subsubsection}{\numberline {3.5.1}Simplesso con variabili free}{25}{subsubsection.3.5.1}%
\contentsline {subsubsection}{\numberline {3.5.2}Problema PLC con simplesso e gomory in salsa teriyaki}{27}{subsubsection.3.5.2}%
\contentsline {subsubsection}{\numberline {3.5.3}Senstivity Analysis}{29}{subsubsection.3.5.3}%
\contentsline {section}{\numberline {4}Grafi}{31}{section.4}%
\contentsline {subsection}{\numberline {4.1}GT}{31}{subsection.4.1}%
\contentsline {subsubsection}{\numberline {4.1.1}Dijkstra}{31}{subsubsection.4.1.1}%
\contentsline {subsubsection}{\numberline {4.1.2}Shortest Path Tree}{33}{subsubsection.4.1.2}%
\contentsline {subsection}{\numberline {4.2}SST}{34}{subsection.4.2}%
\contentsline {subsubsection}{\numberline {4.2.1}Cenni di Base}{34}{subsubsection.4.2.1}%
\contentsline {subsubsection}{\numberline {4.2.2}SST Prim's}{35}{subsubsection.4.2.2}%
\contentsline {subsubsection}{\numberline {4.2.3}SST Da Matrice trovare la soluzione ottimale}{36}{subsubsection.4.2.3}%
\contentsline {subsection}{\numberline {4.3}Max Flow}{37}{subsection.4.3}%
\contentsline {subsubsection}{\numberline {4.3.1}Cenni di Base}{37}{subsubsection.4.3.1}%
\contentsline {subsubsection}{\numberline {4.3.2}Flow Network}{38}{subsubsection.4.3.2}%
\contentsline {subsection}{\numberline {4.4}DP}{40}{subsection.4.4}%
\contentsline {subsubsection}{\numberline {4.4.1}DP Knapsack 0-1 Dynamic Programming}{40}{subsubsection.4.4.1}%
\contentsline {subsubsection}{\numberline {4.4.2}DP: SSP Bellman's-Ford}{42}{subsubsection.4.4.2}%
\contentsline {subsection}{\numberline {4.5}ILP}{44}{subsection.4.5}%
\contentsline {subsubsection}{\numberline {4.5.1}ILP standard B\&B}{44}{subsubsection.4.5.1}%
\contentsline {subsubsection}{\numberline {4.5.2}ILP esercizio standard B\&B}{48}{subsubsection.4.5.2}%
\contentsline {subsubsection}{\numberline {4.5.3}ILP esercizio B\&B 0-1}{50}{subsubsection.4.5.3}%
\contentsline {section}{\numberline {5}GPLK}{52}{section.5}%
\contentsline {subsection}{\numberline {5.1}Dal modello al codice}{52}{subsection.5.1}%
\contentsline {subsubsection}{\numberline {5.1.1}Modello Easy}{52}{subsubsection.5.1.1}%
\contentsline {subsubsection}{\numberline {5.1.2}Caso Particolare 1 Graffa}{53}{subsubsection.5.1.2}%
\contentsline {subsubsection}{\numberline {5.1.3}Caso Particolare 2 Sommatoria doppio insieme}{55}{subsubsection.5.1.3}%
\contentsline {subsection}{\numberline {5.2}Dal codice al modello}{56}{subsection.5.2}%
\contentsline {subsubsection}{\numberline {5.2.1}Normale}{56}{subsubsection.5.2.1}%
\contentsline {section}{\numberline {6}Domande varie di teoria}{57}{section.6}%
\contentsline {subsection}{\numberline {6.1}PLC degenerate}{57}{subsection.6.1}%
\contentsline {subsection}{\numberline {6.2}PLC sensitivty}{58}{subsection.6.2}%
\contentsline {subsection}{\numberline {6.3}B\&B}{58}{subsection.6.3}%
\contentsline {subsection}{\numberline {6.4}PLC minimization}{58}{subsection.6.4}%
\contentsline {subsection}{\numberline {6.5}cutting Plane}{58}{subsection.6.5}%
\contentsline {subsection}{\numberline {6.6}PLC dual}{59}{subsection.6.6}%
\contentsline {subsection}{\numberline {6.7}Dijkstra}{59}{subsection.6.7}%
\contentsline {subsection}{\numberline {6.8}B\&B knapsack}{59}{subsection.6.8}%
\contentsline {subsection}{\numberline {6.9}Branch \& cut}{59}{subsection.6.9}%
\contentsline {subsection}{\numberline {6.10}PLC}{60}{subsection.6.10}%