Abstract
Das kapazitierte Standortproblem, welches in der englischsprachigen Literatur als „Capacitated Facility Location Problem“ (CFLP) bezeichnet wird, ist eine sehr bekannte kombinatorische Optimierungsaufgabe mit zahlreichen Anwendungen in der Produktions- und Distributionsplanung. Das Problem besteht in der Auswahl von Standorten für Depots bzw. Warenlager aus einer gegebenen Menge potentieller Standorte und der Bestimmung der Liefermengen an gegebene Kundenorte derart, dass die Nachfragemengen zu minimalen totalen Kosten — bestehend aus den Kosten des Transports sowie den variablen und fixen Standortkosten — bei Beachtung gegebener Kapazitätsgrenzen für die Umschlagsmengen der Depotstandorte befriedigt werden können. Zur exakten und approximativen Lösung dieser Aufgabe wurden in der Literatur eine Reihe von Verfahren vorgestellt. Exakte Branch-and-Bound-Algorithmen beruhen dabei i. d. R. auf Lagrange- Relaxationen und dem Einsatz von Subgradientenverfahren. Dies hat den Nachteil, dass zum Aufbau des Enumertionsbaumes keine (fraktionalen) primalen Lösungen als Leitlinie zur Verfügung stehen. Mit Hilfe von Verfahren der Spaltengenerierung lässt sich jedoch die zur Lagrange-Schranke gehörige primale Lösung ermitteln. In dieser Arbeit wird ein auf diesem Prinzip beruhendes Branch-and-Bound-Verfahren vorgestellt, wobei vor allem die Untersuchung unterschiedlicher Regeln zur Bestimmung der Verzweigungsvariablen im Vordergrund steht.
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Görtz, S., Klose, A. (2005). Das kapazitierte Standortproblem: Branch-and-Price und die Wahl der Verzweigungsvariable. In: Günther, HO., Mattfeld, D.C., Suhl, L. (eds) Supply Chain Management und Logistik. Physica-Verlag HD. https://doi.org/10.1007/3-7908-1625-6_23
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