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Dynamic programming algorithms for multi-stage safety stock optimization

Content Provider	Springer Nature Link
Author	Minner, Stefan
Copyright Year	1997
Abstract	The task of multi-stage safety stock optimization is very complex. Therefore, simplifying models with specific assumptions are considered. In this paper, the inventory system is controlled by a base-stock policy where each stockpoint of the inventory system follows a periodically reviewed order-up-to policy. End item demands are assumed to be normally distributed. To reduce the occurrences or size and duration of internal and external stockouts, appropriate service level constraints are specified for all items. Applying such a control policy within systems of serial, convergent or divergent structure, solution properties hold which reduce the solution set to a limited number of cut-levels. Dynamic programming allows to evaluate the relevant alternatives with little computational effort. For the serial system, both a forward and a backward recursion with different types of service levels are presented and extended to a backward algorithm for divergent and a forward algorithm for convergent systems. Bounds for the complexity of the algorithms are discussed and numerical examples are presented to demonstrate differences in size and allocation of safety stocks according to the prespecified type of service level.Da das Problem der mehrstufigen Sicherheitsbestandsplanung sehr komplex ist, werden vielfach vereinfachende Modelle mit speziellen Annahmen betrachtet. Im vorliegenden Beitrag arbeitet das Lagerhaltungssystem nach einer Base-Stock Kontrollregel, bei der jeder Bestandspunkt eine periodisch überwachte Bestellgrenzenpolitik verfolgt. Die Endproduktnachfragen werden als normalverteilt angenommen. Für alle Zwischen- und Endprodukte werden Servicegrade zur Begrenzung von internen und externen Fehlmengenereignissen bzw. des Ausmaßes und der Dauer von Fehlbeständen vorgegeben. Bei der Anwendung einer solchen Kontrollregel in seriellen, konvergierenden oder divergierenden Systemen können die durch Sicherheitsbestandshaltung von einem Bestandspunkt abgedeckten Prozeßzeiten nur einige ausgezeichnete Werte annehmen. Mit Hilfe der Dynamischen Programmierung können die relevanten Alternativen mit geringem Rechenaufwand ausgewertet werden. Für serielle Systeme bei unterschiedlichen Typen von Servicegradvorgaben wird sowohl eine Rückwärtsals auch eine Vorwärtsrekursion vorgestellt. Die Rückwärtsrekursion wird auf divergierende und die Vorwärtsrekursion auf konvergierende Systeme erweitert, wobei obere Schranken für die Komplexität der Algorithmen diskutiert werden. Außerdem werden anhand von Beispielen Unterschiede in Verteilung und Höhe von Sicherheitsbeständen in Abhängigkeit vom vorgegebenen Servicegradtyp präsentiert.
Starting Page	261
Ending Page	271
Page Count	11
File Format	PDF
ISSN	01716468
Journal	OR Spectrum
Volume Number	19
Issue Number	4
e-ISSN	14366304
Language	English
Publisher	Springer-Verlag
Publisher Date	1997-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lagerhaltung Sicherheitsbestände Mehrstufige Systeme Dynamische Programmierung Calculus of Variations and Optimal Control Optimization Business/Management Science Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Business, Management and Accounting

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