Unternehmensforschung

, Volume 10, Issue 3, pp 168–189 | Cite as

Beiträge zur Dekomposition von linearen Programmen

  • S. T. Tan
Abhandlungen
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Zusammenfassung

Das Ziel dieser Arbeit besteht vor allem darin, die Zusammenhänge der Dekompositionsmethoden für lineare Programme vonDantzig/Wolfe, Abadie/Williams, Benders, Rosen usw. aufzusuchen. In Kapitel I und III werden diese Methoden mehr oder weniger ausführlich behandelt. Für einige Sätze werden neue Beweise angegeben. In Kapitel II entwickeln wir eine neue Dekompositionsmethode, die aus der Kombination des primaldualen Verfahrens mit derDantzig/Wolfeschen Dekomposition entsteht. Der Idee vonCharnes/Cooper folgend benützen wir „dyadische Transformationen“ in Kapitel IV, um mehrstufige und Transportprobleme durch Dekomposition zu lösen. Schließlich werden in Kapitel V Überlicke über Anwendungen, Erweiterungen für nichtlineare Programmierung und einige Ausblicke gegeben.

Summary

In this paper we are concerned with the decomposition methods ofDantzig/Wolfe, Abadie/Williams, Benders andRosen, particularly to show the relations among them. A new method, the “primal-dual decomposition method” is developed. FollowingCharnes/Cooper, “dyadic transformations” are used to solve various linear programs by decomposition. A survey of extensions and applications is also given.

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Copyright information

© Physical-Verlag 1966

Authors and Affiliations

  • S. T. Tan
    • 1
  1. 1.Mathematisches Institut und Rechenzentrum der Universität ZürichZürich

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