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Transform methodology applied to some inventory problems

Content Provider	Springer Nature Link
Author	Grubbström, Robert W.
Copyright Year	2007
Abstract	In this article we have attempted to demonstrate the use of the Laplace transform, when it is applied to inventory-theoretic models. This is a mathematical methodology for solving differential equations, for studying stability properties of dynamic systems, as a moment-generating function in probability theory, for evaluating the Net Present Value (NPV), and for several other applications. It dates back to the early 18$^{th}$ century. Its most common use today is in electrical engineering, in particular circuit theory. However, in recent decades, its application has been widened to a multitude of economic and managerial problems, especially using it for evaluating payment streams according to the Net Present Value principle (and the related Annuity Stream principle).This article has presented examples of applications to certain inventory problems: A delayed inventory control model A simple stochastic model illustrating the Newsboy Problem in a new setting Saw-tooth patterned inventory cycles, including the Economic Production Quantity (EPQ), a Supply Chain problem and a basic model of remanufacturing Material Requirements Planning Theory (MRP). Certain theorems of the Laplace transform have proved to be useful frequently, such as time translation, final value, and NPV.In diesem Beitrag wurde gezeigt, wie die Laplace Transformation für die Formulierung von Modellen der Lagerhaltungstheorie genutzt werden kann. Obwohl als mathematisches Konzept für die Lösung von Differentialgleichungen entwickelt, wird die Laplace Transformation heute für die Modellierung volks-und betriebswirtschaftlicher Probleme besonders in den Fällen eingesetzt, in denen Zahlungsströme nach dem Kapitalwert bewertet werden sollen.Als Beispiele der Übertragung auf Lagerhaltungsprobleme sind dargestellt worden: ein Modell zur Kontrolle verspäteter Lagerzugänge ein einfaches stochastisches Modell, welches die Formulierung des Zeitungsjungen-Problems in neuem Gewand erscheinen lässt das Harris-Modell unter Erweiterung der Einbettung in eine Supply Chain und der Bestimmung der Wiederauflage von Losen Sowie Fragestellungen der Materialbedarfsplanung. Bestimmte Theoreme der Laplace Transformation haben sich bei der Anwendung auf Fälle von Zeitverschiebungen, Endwert-und Kapitalwertbestimmungen oft als nützlich erwiesen.
Starting Page	297
Ending Page	324
Page Count	28
File Format	PDF
ISSN	00442372
Journal	Zeitschrift für Betriebswirtschaft
Volume Number	77
Issue Number	3
Language	German
Publisher	Gabler Verlag
Publisher Date	2007-01-01
Publisher Place	Wiesbaden
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Production Management Laplace transform economic order quantity remanufacturing supply chain material requirements planning net present value annuity stream Business/Management Science Management Organization/Planning Accounting/Auditing Personnel Management Production/Logistics
Content Type	Text
Resource Type	Article
Subject	Business and International Management Economics and Econometrics

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