Diskrete Optimierung
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Neben den Problemen der linearen Optimierung hat wohl die diskrete Optimierung unter den mathematischen Optimierungsmethoden die groBte praktische Aufmerk- samkeit gefunden. Das ist sicher nicht zuletzt in der Tat- sache begriindet, daB viele Modelle der linearen Optimie- rung automatisch zu Aufgaben der diskreten Optimierung fUhren, wenn die Ganzzahligkeit fUr gewisse Modellvaria- bIen gefordert wird. Eine derartige Ganzzahligkeitsforde- rung ergibt sich aber haufig aus der okonomischen Pro- blemsituation. So lassen sich z. B. bei der Losung eines Transportproblems nur ganze Anzahlen von Gtiterwagen einsetzen; die Planung eines Investitionsprojektes laBt nur den Einsatz ganzer Zahlen von Maschinen oder den Bau ganzer Zahlen von Fabrikanlagen 6konomisch rele- vant erscheinen; die Planung des Bedarfs von Arbeits- kraften kann mit der Ganzzahligkeitsforderung verbunden sein. Daher ist es keineswegs vielfach die Frage, ob die Ganzzahligkeit gewisser Modellvariablen okonomisch als gegeben angesehen werden kann. VielIllJilhr werfen die sich beim LosungsprozeB ergebenden Komplikationen das Problem auf, ob der Verzicht auf diese Ganzzahligkeits- forderung okonomisch moglich erscheint. Weiterhin hat eine Reihe von diskreten Optimierungsmodellen kombi- natorischen Charakters das Interesse der Anwender an derartigen Optimierungsmethoden gefordert, da sie ein- fache und praktisch wichtige Problemsituationen be- schreiben. Methoden der diskreten Optimierung sind heute bereits Gegenstand einer Ftille von Publikationen. Es gibt Mono- graphien und umfassende Darstellungen selbst zu Teil- Vorwort 4 problemen der diskreten Optimierung und ihrer Anwen- dung. Daher bin ich wohl dem Leser die Antwort auf die Frage schuldig, von welcher Zielstellung ich im folgenden ausgehen mochte.
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