\contentsline {section}{\numberline {1}Modelli}{3}{}%
\contentsline {subsection}{\numberline {1.1}Cenni di Base}{3}{}%
\contentsline {subsection}{\numberline {1.2}Esercizi}{5}{}%
\contentsline {subsubsection}{\numberline {1.2.1}Problema con Delta}{5}{}%
\contentsline {subsubsection}{\numberline {1.2.2}Problema con massima distanza}{6}{}%
\contentsline {subsubsection}{\numberline {1.2.3}Problema Variabile Triplo indice}{7}{}%
\contentsline {subsubsection}{\numberline {1.2.4}Problema di Trasporto}{9}{}%
\contentsline {subsubsection}{\numberline {1.2.5}Problema di Stoccaggio}{11}{}%
\contentsline {subsubsection}{\numberline {1.2.6}Problema di Stoccaggio 2}{12}{}%
\contentsline {section}{\numberline {2}Forme: Standard, Canonica, Generale}{13}{}%
\contentsline {subsection}{\numberline {2.1}Standard $\Rightarrow $ Canonica}{13}{}%
\contentsline {subsection}{\numberline {2.2}Generale $\Rightarrow $ Standard}{13}{}%
\contentsline {subsection}{\numberline {2.3}Esercizio Trasformazione Gran Fritto Misto}{14}{}%
\contentsline {section}{\numberline {3}Matrici : LP, ILP}{15}{}%
\contentsline {subsection}{\numberline {3.1}Fondamenti Concettuali}{15}{}%
\contentsline {subsubsection}{\numberline {3.1.1}Quale Simplesso?}{15}{}%
\contentsline {subsection}{\numberline {3.2}LP}{15}{}%
\contentsline {subsubsection}{\numberline {3.2.1}Simplesso}{15}{}%
\contentsline {subsubsection}{\numberline {3.2.2}Simplesso Duale}{16}{}%
\contentsline {subsubsection}{\numberline {3.2.3}2Fasi}{17}{}%
\contentsline {subsubsection}{\numberline {3.2.4}Duale del problema}{19}{}%
\contentsline {subsection}{\numberline {3.3}Rappresentazione Grafica}{20}{}%
\contentsline {subsection}{\numberline {3.4}ILP}{22}{}%
\contentsline {subsubsection}{\numberline {3.4.1}Tagli di Gomory}{22}{}%
\contentsline {subsection}{\numberline {3.5}Esercizi Particolari}{24}{}%
\contentsline {subsubsection}{\numberline {3.5.1}Simplesso con variabili free}{24}{}%
\contentsline {subsubsection}{\numberline {3.5.2}Problema PLC con simplesso e gomory in salsa teriyaki}{26}{}%
\contentsline {subsubsection}{\numberline {3.5.3}Senstivity Analysis}{28}{}%
\contentsline {section}{\numberline {4}Grafi}{30}{}%
\contentsline {subsection}{\numberline {4.1}GT}{30}{}%
\contentsline {subsubsection}{\numberline {4.1.1}Dijkstra}{30}{}%
\contentsline {subsubsection}{\numberline {4.1.2}Shortest Path Tree}{32}{}%
\contentsline {subsection}{\numberline {4.2}SST}{33}{}%
\contentsline {subsubsection}{\numberline {4.2.1}Cenni di Base}{33}{}%
\contentsline {subsubsection}{\numberline {4.2.2}SST Prim's}{34}{}%
\contentsline {subsubsection}{\numberline {4.2.3}SST Da Matrice trovare la soluzione ottimale}{35}{}%
\contentsline {subsection}{\numberline {4.3}Max Flow}{36}{}%
\contentsline {subsubsection}{\numberline {4.3.1}Cenni di Base}{36}{}%
\contentsline {subsubsection}{\numberline {4.3.2}Flow Network}{37}{}%
\contentsline {subsection}{\numberline {4.4}DP}{39}{}%
\contentsline {subsubsection}{\numberline {4.4.1}DP Knapsack 0-1 Dynamic Programming}{39}{}%
\contentsline {subsubsection}{\numberline {4.4.2}DP: SSP Bellman's-Ford}{41}{}%
\contentsline {subsection}{\numberline {4.5}ILP}{43}{}%
\contentsline {subsubsection}{\numberline {4.5.1}ILP standard B\&B}{43}{}%
\contentsline {subsubsection}{\numberline {4.5.2}ILP esercizio standard B\&B}{47}{}%
\contentsline {subsubsection}{\numberline {4.5.3}ILP esercizio B\&B 0-1}{49}{}%
\contentsline {section}{\numberline {5}GPLK}{51}{}%
\contentsline {subsection}{\numberline {5.1}Dal modello al codice}{51}{}%
\contentsline {subsubsection}{\numberline {5.1.1}Modello Easy}{51}{}%
\contentsline {subsubsection}{\numberline {5.1.2}Caso Particolare 1 Graffa}{52}{}%
\contentsline {subsubsection}{\numberline {5.1.3}Caso Particolare 2 Sommatoria doppio insieme}{54}{}%
\contentsline {subsection}{\numberline {5.2}Dal codice al modello}{55}{}%
\contentsline {subsubsection}{\numberline {5.2.1}Normale}{55}{}%
\contentsline {section}{\numberline {6}Domande varie di teoria}{56}{}%
\contentsline {subsection}{\numberline {6.1}PLC degenerate}{56}{}%
\contentsline {subsection}{\numberline {6.2}PLC sensitivty}{57}{}%
\contentsline {subsection}{\numberline {6.3}B\&B}{57}{}%
\contentsline {subsection}{\numberline {6.4}PLC minimization}{57}{}%
\contentsline {subsection}{\numberline {6.5}cutting Plane}{57}{}%
\contentsline {subsection}{\numberline {6.6}PLC dual}{58}{}%
\contentsline {subsection}{\numberline {6.7}Dijkstra}{58}{}%
\contentsline {subsection}{\numberline {6.8}B\&B knapsack}{58}{}%
\contentsline {subsection}{\numberline {6.9}Branch \& cut}{58}{}%
\contentsline {subsection}{\numberline {6.10}PLC}{58}{}%