Lecture Notes in Economics and Mathematical Systems

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1 Lecture Notes in Economics and Mathematical Systems 520 Founding Editors: M. Beckmann H. P. Kiinzi Managing Editors: Prof. Dr. G. Fandel Fachbereich Wirtschaftswissenschaften Fernuniversitat Hagen Feithstr. 140/AVZ 11,58084 Hagen, Germany Prof. Dr. W. Trockel Institut fur Mathematische Wirtschaftsforschung (IMW) Universitat Bielefeld Universitatsstr. 25, Bielefeld, Germany Co-Editors: C. D. Aliprantis Editorial Board: A. Basile, A. Drexl, G. Feichtinger, W Giith, K. Inderfurth, P. Korhonen, W. Kiirsten, U. Schittko, P. SchOnfeld, R. Selten, R. Steuer, F. Vega-Redondo

2 Springer-Verlag Berlin Heidelberg GmbH

3 Bodo Glaser Efficiency versus Sustainability in Dynamic Decision Making Advances in Intertemporal Compromising Springer

4 AuthOf Dr. Bodo Glaser Chair for Operations Research Department of Business Administration and Economics University of Saarland Im Stadtwald Saarbrticken Germany Cataloging-in-PubIication data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Glaser, Bodo: Efficiency versus sustainability in dynamic decison making: advances in intertemporal compromising / Bodo Glaser. - Berlin; Heidelberg; New York; Barcelona ; Hong Kong ; Landon ; Milan ; Paris; Tokyo: Springer, 2002 (Lecture notes in economics and mathematical systems ; 520) ISBN ISBN (ebook) DOI / ISSN ISBN This work is subject to copyright. AII rights are reserved, whether the whoje Of paft of the material is concerned, specifically the rights of translation, reprinting, re-use of i liustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 2002 Originally published by Springer-Verlag Berlin Heidelberg New York in 2002 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such namcs are exempt from the relevant protective laws and regulations and thcreforc frec for general use. Typcsetting: Camera ready by author Cover design: Erich Kirchner, Heidclberg Printed on acid-free paper SPIN: /3142/du

5 Preface To all who taught me, and to all who will. Over the past fifteen years the notions of efficiency and sustainability have, more than any others, influenced the academic and public discussion concerning the intertemporal allocation of resources, especially as regards the economics of growth and environment. This treatise formally develops and counterposes these notions by means of the construct of a trajectorial objective, which is here developed, along with its implications, as a natural advance upon the classical scalar objective. In the course of this study it becomes clear that efficiency and sustainability are by no means identical, given that efficiency, on the one hand, is the concept for avoiding wasteful behavior, and sustainability, on the other, is the concept for ensuring that certain critical aspiration levels, which usually reflect the wish for survival, are maintained. Nonetheless, contrary to what may be assumed, these two concepts do not generally yield mutually exclusive solutions; in fact, they can be combined to complement each other in the quest for unimprovable long-term solutions which sustain given and necessary aspiration levels. This treatise develops and analyzes dynamic decision models (DDM) with one trajectorial objective according to the methodology of multicriteria decision making (MCDM). Moreover, introducing the method of distance maximization crucially augments MCDM and proves to be invaluable for DDMs in the case of a nonexistent utopia trajectory as well as in the case of sustainability as objective. Additionally, dynamic decision models which concomitantly pursue multiple objectives are here analyzed, with special emphasis given to hybrid models with scalar and trajectorial objectives as well as models with multiple trajectorial objectives.

6 VI Although all steps of this treatise are accompanied by numerical examples taken from the field of economics, the concepts and models here presented are also of significant relevance to the fields of science and technology as well as business administration; therefore, a brief sketch of applications in the respectively above-mentioned fields is given in the introduction to Chapters 5 and 6 as well as in all three sections of Chapter 7. To accommodate different readerships, discrete time and continuous time setting are always developed parallely throughout this treatise. All 3D-graphics in Chapters 6 and 7 are available in color and rotatable at First and foremost I wish to thank my pater academicus Prof. Dr. Werner Dinkelbach for his unfailing support of this research project and for granting me a great deal of freedom and responsibility in my work at the Chair for Operations Research at the University of Saarland. Further, I am indebted to Prof. Dr. Willy Spanjers, who also refereed this treatise, and to Prof. Dr. Horst Glaser and Dr. Lars Petersen for taking part in the dissertation committee. Jiirgen Marx, who devoted much of his valuable time to proofreading this treatise with utmost precision, and PD Dr. Andreas Kleine were a great support - especially thanks to the "Friday Think Tank" - through their sustained critical acumen and readiness for discussion. To Karin Hunsicker I am indebted for many years of knowledgeable assistance and unflagging encouragement. I am grateful to Dr. Andrea Piro, Dr. Bernd Serf, Dr. Markus Riess, Dr. Michael Linke and Dr. Thomas Latz for many helpful comments, to Rico Kutscher for being an able sparring partner, and to Eva Maria Kupper and Johannes Wirth for last-minute technical support. My thanks also go the people at BR3 for the Space Night program, which accompanied me through many a night's work. For sustained and successful health support I wish to express my gratitude to Dr.-lng. Jewgeni Awerbuch. I thank my family for their continued encouragement of my academic career. My wife, friend and academic counsellor Stephanie deserves my utmost gratitude for many productive walks as well as for her patience, loving support and many sacrifices. Saarbriicken, April 2002 Bodo Glaser

7 Contents 1 Introduction 1 I Decision Theoretical Foundation 5 2 Fundamentals of Decision Making 2.1 Structure and Classification of Decision Models 2.2 The Set of Alternatives. 2.3 Kinds of Objectives. 2.4 Optimality Fundamentals of Multi-criteria Decision Making The General MODM-model Dominance and Efficiency Compromise Methods Method of Weighting Objective Functions Method of Weighted Distance Functions Distance-minimization Method Distance-maximization Method Synopsis of Distance-based Methods 72

8 VIII Contents II Dynamic Decision Making 75 4 Fundamentals of Dynamic Decision Making The Set of Alternatives Basic Types of Objectives in Dynamic Decision Making 88 5 Type A Objective: 'The Destination Matters' Problem Formulation Refinements of the General Formulation Optimality Type B Objective: 'The Journey is the Goal' Problem Formulation Dynamic Dominance and Efficiency Compromise Models Method of Weighting Periodic Objectives Method of Weighted Periodic Distances Sustainability as Objective A Formal Definition Satisficing Objective without Maximizing Behavior Satisficing Objective with Maximizing Behavior Afterthought Multiple Objectives in Dynamic Decision Making Multiple Type A Objectives Multiple Objectives of Hybrid Types Problem Formulation Efficiency Aspects Compromise Models 207

9 Contents IX Sustainability Revisited 7.3 Multiple Type B Objectives Problem Formulation Efficiency Aspects Compromise Models Sustainability Revisited 8 Concluding Remarks List of Figures Symbols and Notation Bibliography Index

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