Dynamic Programming of Economic Decisions
Dynamic Programming is the analysis of multistage decision in the sequential mode. It is now widely recognized as a tool of great versatility and power, and is applied to an increasing extent in all phases of economic analysis, operations research, techno
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Herausgegeben von I Edited by
M. Beckmann, Bonn' R. Henn, Karlsruhe· A. Jaeger, Cincinnati W. Krelle, Bonn' H. P. Kiinzi, Zurich K. Wenke, Ludwigshafen· Ph. Wolfe, Santa Monica Geschiiftsfohrende Herausgeber I Managing Editors
W. Krelle . H. P. Kunzi
Martin J. Beckmann
Dynamic Programming of Economic Decisions
Springer-Verlag New York Inc. 1968
Professor Dr. MARTIN J. BECKMANN Institut fUr Okonometrie und Unternehmensforschung der Universitat Bonn and Brown University, Providence, R.1.
ISBN 978-3-642-86451-3 DOl 10.1007/978-3-642-86449-0
ISBN 978-3-642-86449-0 (eBook)
The use of general descriptive names, trade names, trade marks, etc. in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. All rights reserved. No part of this book may be translated or reproduced in any form without written permission from Springer-Verlag. e by Springer-Verlag Berlin· Heidelberg 1968. Library Softcover reprint of the hardcover 1st edition 1968 of Congress Catalog Card Number 68-21991. Title-No. 6484
Parentibus et Soceris
Preface Dynamic Programming is the analysis of multistage decision in the sequential mode. It is now widely recognized as a tool of great versatility and power, and is applied to an increasing extent in all phases of economic analysis, operations research, technology, and also in mathematical theory itself. In economics and operations research its impact may someday rival that of linear programming. The importance of this field is made apparent through a growing number of publications. Foremost among these is the pioneering work of Bellman. It was he who originated the basic ideas, formulated the principle of optimality, recognized its power, coined the terminology, and developed many of the present applications. Since then mathematicians, statisticians, operations researchers, and economists have come in, laying more rigorous foundations [KARLIN, BLACKWELL], and developing in depth such application as to the control of stochastic processes [HoWARD, JEWELL]. The field of inventory control has almost split off as an independent branch of Dynamic Programming on which a great deal of effort has been expended [ARRoW, KARLIN, SCARF], [WIDTIN] , [WAGNER]. Dynamic Programming is also playing an increasing role in modem mathematical control theory [BELLMAN, Adaptive Control Processes (1961)]. Some of the most exciting work is going on in adaptive programming which is closely related to sequential statistical analysis, particularly in its Bayesian form. In this monograph the reader is introduced to the basic ideas of Dynamic Programming. An attempt is made to show the breadth of this method by a careful exposition of its principles followed by some typical applications to economic analysis, operations research and decisions in general. Some effort has been made to give a systematic exposition of the various possibilities: discrete and continuous seq
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