Inventory-Production Theory A Linear Policy Approach
The term inventory-production theory is not well defined. It com prises e. g. such models like cash balance models, production smoothing models and pure inventory models. We shall here mainly be concerned with stochastic dynamic problems and shall give e
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151
Christoph A. SchneeweiB
Inventory-Production Theory A Linear Policy Approach
Springer-Verlag
Editorial Board H. Albach A. V. Balakrishnan
M. Beckmann (Managing Editor)
P. Dhrymes J. Green W. Hildenbrand W. Krelle H. P. Kunzi (Managing Editor) K. Ritter R. Sato H. Schelbert P. Schonfeld
Managing Editors Prof. Dr. M. Beckmann Brown University Providence, RI 02912/USA
Prof. Dr. H. P. KOnzi Universitat ZOrich 8090 ZOrich/Schweiz
Author Christoph A. SchneeweiB Freie Universitat Berlin Fachbereich Wirtschaftswissenschaften Fachrichtung Operations Research Thielallee 66 1000 Berlin
Library of Congress Cataloging in Publication Data
Schneeweiss. Ch Inventory-production theory. (Lecture notes in economics and mathematical systems 151 : Operations research) Bibliography: p. Includes index. 1. Production planning--Mathematical models. 2. Inventory control-Mathematical models. 3. Linear programming. I. Title. II. Series: Lecturennotes in economics and mathematical systems ; 151. TS176.S36 658.7'87 77-13254
AMS Subject Classifications (1970): 90-02,90830, 49C99
ISBN-13: 978-3-540-08443-3 e-ISBN-13: 978-3-642-95311-8 001: 10.1007/978-3-642-95311-8 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin Heidelberg 1977
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PRE F ACE This treatise tries to give a coherent account of part of the work that has been done during recent years at the "Fachrichtung Operations Research" of the Free University Berlin. It is dealing with what shall be called the "linear policy approach" to stochastic inventory-production problems: The treatise investigates the efficiency of certain types of inventoryproduction models in which the optimal non-linear ordering or production policy is replaced by a linear one. A linear policy not only reduces the computational burden considerably, but also allows to a certain extent for the existence of dynamic certainty equivalents. I.e., roughly speaking, the optimal production policy remains optimal if one replaces the stochastic sequence of demand by its forecasts. Thus, if for a stochastic dynamic optimization problem only forecasts are available the question arises whether a linear policy can be shown to be more adaquate than a non-linear policy.
Part of this account has been written during the author's stay at the University of Cambridge. He is particularly grateful for the hospitality of the Control Engineering Group of the University Engineering Department and to Clare Hall, the college to which the author was an Associated Member during winter 1974/75. Furthermore the author wants to express his gratitude to the members of
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