This volume collects research papers addressing topical issues in economics and management with a particular focus on dynamic models which allow to analyze and foster the decision making of firms in dynamic complex environments. The scope of the contributions ranges from daily operational challenges firms face to strategic choices in dynamic industry environments and the analysis of optimal growth paths. The volume also highlights recent methodological developments in the areas of dynamic optimization, dynamic games and meta-heuristics, which help to improve our understanding of (optimal) decision making in a fast evolving economy.

Since the days of Lev Pontryagin and his associates, the discipline of Optimal Control has enjoyed a tremendous upswing - not only in terms of its mathematical foundations, but also with regard to numerous fields of application, which have given rise to highly active research areas. Few scholars, however, have been able to make contributions to both the mathematical developments and the (socio-)economic applications; Vladimir Veliov is one of them. In the course of his scientific career, he has contributed highly influential research on mathematical aspects of Optimal Control Theory, as well as applications in Economics and Operations Research. One of the hallmarks of his research is its impressive breadth. This volume, published on the occasion of his 65th birthday, accurately reflects that diversity. The mathematical aspects covered include stability theory for difference inclusions, metric regularity, generalized duality theory, the Bolza problem from a functional analytic perspective, and fractional calculus. In turn, the book explores various applications of control theory, such as population dynamics, population economics, epidemiology, optimal growth theory, resource and energy economics, environmental management, and climate change. Further topics include optimal liquidity, dynamics of the firm, and wealth inequality.

This volume collects research papers addressing topical issues in economics and management with a particular focus on dynamic models which allow to analyze and foster the decision making of firms in dynamic complex environments. The scope of the contributions ranges from daily operational challenges firms face to strategic choices in dynamic industry environments and the analysis of optimal growth paths. The volume also highlights recent methodological developments in the areas of dynamic optimization, dynamic games and meta-heuristics, which help to improve our understanding of (optimal) decision making in a fast evolving economy.

The first Joint Meeting of the Austrian and Swiss Operations Research Societies was held at the University of Technology in Vienna, Austria, from 22-24 September 1980. A selection of the papers then presented are published in this volume. The papers included provide a picture of Operations Research as a discipline comprehending various methods and models. The volume is divided into two parts. The first part contains papers on mathematical programming and optimal control theory. Moreover, two papers on decision and game theory are included as well as two on biomathematical to~ics. Being more heterogeneous, the second part, on stochastic models, includes such topics as queueing theory, econometrics and time series analysis. As a special feature of the symposium, a series of applications of OR models in energy planning were discussed, e.g., load and demand forecasting, power distribution and extension planning, reliability and work-safety, etc. These papers have been incorporated into parts one and two according to the models used. GUSTAV FEICHTINGER PETER !C ALL Institut fUr Okonometrie und Institut fUr Operations Research und Operations Research mathematische Methoden der Wirtschafts- Technische UniversitHt wissenschaften Wien UniversitHt ZUrich November 198 I ix Gustav Feichtinger and Peter Kall (eds.), Operations Research in Progress, ix..

Franz Ferschl is seventy. According to his birth certificate it is true, but it is unbelievable. Two of the three editors remembers very well the Golden Age of Operations Research at Bonn when Franz Ferschl worked together with Wilhelm Krelle, Martin Beckmann and Horst Albach. The importance of this fruitful cooperation is reflected by the fact that half of the contributors to this book were strongly influenced by Franz Ferschl and his colleagues at the University of Bonn. Clearly, Franz Ferschl left his traces at all the other places of his professional activities, in Vienna and Munich. This is demonstrated by the present volume as well. Born in 1929 in the Upper-Austrian Miihlviertel, his scientific education brought him to Vienna where he studied mathematics. In his early years he was attracted by Statistics and Operations Research. During his employment at the Osterreichische Bundeskammer fUr Gewerbliche Wirtschaft in Vienna he prepared his famous book on queueing theory and stochastic processes in economics. This work has been achieved during his scarce time left by his duties at the Bundeskammer, mostly between 6 a.m. and midnight. All those troubles were, however, soon rewarded by the chair of statistics at Bonn University. As a real Austrian, the amenities of the Rhineland could not prevent him from returning to Vienna, where he took the chair of statistics.

Dynamic optimization is rocket science - and more. This volume teaches researchers and students alike to harness the modern theory of dynamic optimization to solve practical problems. These problems not only cover those in space flight, but also in emerging social applications such as the control of drugs, corruption, and terror. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. The authors celebrate Pontryagin's Maximum Principle - that crowning intellectual achievement of human understanding. The rich theory explored here is complemented by numerical methods available through a companion web site.

Franz Ferschl is seventy. According to his birth certificate it is true, but it is unbelievable. Two of the three editors remembers very well the Golden Age of Operations Research at Bonn when Franz Ferschl worked together with Wilhelm Krelle, Martin Beckmann and Horst Albach. The importance of this fruitful cooperation is reflected by the fact that half of the contributors to this book were strongly influenced by Franz Ferschl and his colleagues at the University of Bonn. Clearly, Franz Ferschl left his traces at all the other places of his professional activities, in Vienna and Munich. This is demonstrated by the present volume as well. Born in 1929 in the Upper-Austrian Miihlviertel, his scientific education brought him to Vienna where he studied mathematics. In his early years he was attracted by Statistics and Operations Research. During his employment at the Osterreichische Bundeskammer fUr Gewerbliche Wirtschaft in Vienna he prepared his famous book on queueing theory and stochastic processes in economics. This work has been achieved during his scarce time left by his duties at the Bundeskammer, mostly between 6 a.m. and midnight. All those troubles were, however, soon rewarded by the chair of statistics at Bonn University. As a real Austrian, the amenities of the Rhineland could not prevent him from returning to Vienna, where he took the chair of statistics.

Yom 28. - 31. August 1990 fand die 19. Jahrestagung der Deutschen Gesellschaft fur Operations Research e. V. an der Wirtschaftsuniversitat Wien statt. Erstmals wurde diese Jahrestagung zusammen mit den anderen deutschsprachigen OR-Gesellschaften, der Gesell- schaft fur Mathematik, Okonomie und Operations Research (GMOOR), der Osterreichi- schen Gesellschaft fur Operations Research (OGOR) und der Schweizerischen Vereinigung fur Operations Research (SVOR) abgehalten. Diese internationale Tagung stand unter dem Titel Operations Research 1990. Fast 1000 Teilnehmer aus 38 Lander machten die Tagung zu einem internationalen GroBereignis. Am stiirksten vertreten waren dabei die Lander BRD (mit 381 Teilnehmern), Osterreich (91), Niederland~ (57), USA (44), Schweiz (38), Italien (35) sowie Kanada (23). Dank der geiinderten politischen Lage konnten knapp 100 Teilnehmer aus den (ehemaligen) sozialistischen Staaten die Tagung besuchen. Dies wurde ermoglicht dank der vielfiiltigen finanziellen Unterstiitzungen durch die Privatwirtschaft und durch das osterreichische Bundesministerium fur Wissenschaft und Forschung. Die Operations Research Proceedings 1990 dokumentieren nur einen kleinen Teil der iiber 600 Vortrage. Von den zur Publikation eingereichten Langfassungen konnten aufgrund der beschriinkten Seitenzahl nur 50 % angenommen werden. Zum groBen Bedauern des Pro- grammausschusses waren aufgrund der beschriinkten Seitenzahl von einer Ablehnung auch ausgezeichnete Manuskripte betroffen. Allein die Veroffentlichung der Kurzfassungen aller prasentierten Vortriige Mtte den Proceedingsband gesprengt. Aus diesem Grunde werden in diesen Proceedings erstmals keine Kurzfassungen publiziert und damit auf eine vollstandige Dokumentation der Tagung verzichtet. Es solI aber hier auf zwei weitere Publikationen hin- gewiesen werden, in denen Vortrage der Tagung Operations Research 90 enthalten sind.

The first Joint Meeting of the Austrian and Swiss Operations Research Societies was held at the University of Technology in Vienna, Austria, from 22-24 September 1980. A selection of the papers then presented are published in this volume. The papers included provide a picture of Operations Research as a discipline comprehending various methods and models. The volume is divided into two parts. The first part contains papers on mathematical programming and optimal control theory. Moreover, two papers on decision and game theory are included as well as two on biomathematical to~ics. Being more heterogeneous, the second part, on stochastic models, includes such topics as queueing theory, econometrics and time series analysis. As a special feature of the symposium, a series of applications of OR models in energy planning were discussed, e.g., load and demand forecasting, power distribution and extension planning, reliability and work-safety, etc. These papers have been incorporated into parts one and two according to the models used. GUSTAV FEICHTINGER PETER !C ALL Institut fUr Okonometrie und Institut fUr Operations Research und Operations Research mathematische Methoden der Wirtschafts- Technische UniversitHt wissenschaften Wien UniversitHt ZUrich November 198 I ix Gustav Feichtinger and Peter Kall (eds.), Operations Research in Progress, ix..

The last fifteen or twenty years have been marked by fundamental advances in the sources of complex behavior in micro- and macro-economics, in the practical and methodological implications of such behavior, and in the methods and tools appropriate to cope with them. Much of these developments have been driven by the recognition and acceptance by economists of approaches initiated in other fields - such as non-linear dynamics, statistical physics, network theory, biology, computer science, and the use of computational methods as problem-solving tools - giving rise to important and innovative impulses to economic thinking.
The sixteen papers in this book -- the fourteenth volume in the series International Symposia in Economic Theory and Econometrics - reflect from various perspectives this recent evolution. They are the outgrow from a selection of communications presented at the COMPLEXITY2000 workshop held in Aix en Provence, France, 4-6 May 2000 - a workshop that brought together, from twenty-two nations, almost seventy economists, mathematicians, biologists and physicists interested in complex phenomena. All papers were strictly refereed in the intended tradition of the series: to provide journal quality collections of research papers of unusual importance in areas of currently highly visible activity within the economics profession.
With its selection of articles, the book presents an overview of advanced contributions to complexity in economics and social system, such as chaotic dynamics and multiple equilibria, agent-based models, applications of genetic algorithms, non-equilibrium macro-dynamics, information transmission, learning mechanisms. Although the papers addresseconomic problems, the authorship and the perspectives presented are interdisciplinary and provide therefore a number of innovative insights and solutions to classical or new questions.

Dynamic optimization is rocket science and more. This volume teaches how to harness the modern theory of dynamic optimization to solve practical problems, not only from space flight but also in emerging social applications such as the control of drugs, corruption, and terror. These innovative domains are usefully thought about in terms of populations, incentives, and interventions, concepts which map well into the framework of optimal dynamic control. This volume is designed to be a lively introduction to the mathematics and a bridge to these hot topics in the economics of crime for current scholars. We celebrate Pontryagin s Maximum Principle that crowning intellectual achievement of human understanding and push its frontiers by exploring models that display multiple equilibria whose basins of attraction are separated by higher-dimensional DNSS "tipping points." That rich theory is complemented by numerical methods available through a companion web site."

Die Bevolkerungswissenschaft hat in den vergangenen Jahrzehnten einen l enormen Aufschwung genommen. Da die Demographie eine eigenstandige Wissenschaft bildet, kann heute kaum mehr geleugnet werden. Zumindest innerhalb des deutschen . Sprachraumes gibt es den ausgebildeten Bevolkerungs- wissenschaftler jedoch nicht. Hierzulande sind es Vertreter benachbarter Substanz- und Formalwissenschaften, welche demographische Problemstellungen behandeln. Ein entscheidendes Bindeglied zwischen diesen aus verschiedenen Lagern . stammenden "Demographen" ist die Beherrschung der grundlegenden Begriffsbildungen, Modelle und Methoden zur Analyse demographischer Phiinomene. Mit diesem RUstzeug, das als Grundsubstanz aller Bevolkerungswissenschaftler anzusehen ist, beschiiftigen sich die vorliegenden AusfUhrungen. Ihr Ziel ist erreicht, wenn dem Leser die N6twendigkeit der Analyse und des Modellbaues bei der Losung demographischer Fragen einsichtig wird. Bevolkerungsprobleme lassen sich haufig nur dann erfolgversprechend behandeln, wenn Vokabular und Grammatik der Sprache der Formaldemographie bzw. Bevolkerungsmathematik beherrscht werden. Nun existieren zwar einige hervorragende fremdsprachige BUcher zur formalen Demographie (Pressat, 1969, Henry, 1972, Keyfitz, 1968a und 1977, Pollard, 1973, Barclay, 1958, Coale, 1972) aber kein deutsch- sprachiges, welches eine ausgewogene EinfUhrung in die Formaldemographie vermittelt. Es scheint an der Zeit, eine mit schwerwiegenden demographischen Problemen konfrontierte Generation von Bevolkerungsforschern mit einem Lehrbuch auszuriisten, das einen formal orientierten Einstieg in die grundlegen- den Konzepte und Modelle der Demographie vermitteln soIl. Aufbau und Aus- wahl des Stoffes waren dabei vorwiegend durch didaktische Gesichtspunkte bestimmt. Keines der drei am Markt betindlichen Bevolkerungsstatistik-BUcher erflillt obige Intentionen ganz.

Die Operations Research Proceedings 1989 dokumentieren die Vortrage, die auf der 18. Jahrestagung der Deutschen Gesellschaft fur Operations Research in der Zeit vom 13. bis 15. September 1989 gehalten worden sind. In dem Band sind die Fassungen von 5 Plenar- und 105 Fachvortragen enthalten, von denen 60 in Lang-, der Rest in Kurzfassungen aufgenommen sind. Im einzelnen sind Beitrage zu folgenden Teilgebieten zusammengestellt: - Operations Research in der Industrie - Operations Research in Banken und Versicherungen - Produktion - Marketing - Logistik und Verkehr - Statistik, Datenanalyse und Prognose - Organisation und Entscheidungstheorie - Decision Support-Systeme und Kunstliche Intelligenz - Wirtschaftsinformatik - Stochastische Prozesse einschl. Zuverlassigkeits- und Bedienungstheorie - Mathematische Optimierung - Spieltheorie - Kontrolltheorie

Die Bevolkerungsmathematik hat im deutschsprachigen Raum in den letzten Jahrzehnten - etwa im Gegensatz zur Entwicklung in Frankreich und in den USA - keinen rechten AnschluB an eine nicht unbedeutende Tradition finden konnen. Die vorliegende Arbeit mochte Probleme der demographischen Analyse erneut aufgreifen, diesmal jedoch unter Heran- ziehung von Begriffsbildungen aus der Theorie stochastischer Prozesse. Die im folgenden vorgeschlagene stochastische Modellierung demogra- phischer Phanomene solI einerseits dem Bevolkerungsstatistiker den Zu- gang zu den oft kniffligen Fragen der formal en Demographie auf einheit- licher Basis exakter und damit auch eleganter gestalten. Es ist die An- sicht des Autors, daa viele bevolkerungsstatistische Problemstellungen erst 1m Rahmen stochastischer Prozesse ihre adaquate Behandlung erfah- ren. Zum anderen liefert ein hier zu leis tender statistischer tlberbau der Demographie didaktisch abgerundete Anwendungsbeispiele der rasch an Bedeutung gewinnenden Theorie der Zufallsprozesse. Das Vorhaben dieser Arbeit besteht darin, zu zeigen, daa die sto- chastisch-dynamische Betrachtungsweise demographischer Vorgange nicht nur ein tragfahiges Fundament ftir die Vielfalt bevolkerungsmathema- tischer Modelle abgeben kann, sondern auch die Behandlung neuartiger genuiner Fragenkomplexe gewahrleistet. Die Untersuchung gliedert sich in drei Teile. In der am Beginn stehenden Mikrotheorie fungieren als ProzeSzustande jene, die von demographischen Individuen angenommen werden konnen, also etwa der Familienstand einer Person. Hingegen wer- den beim Zustandsbegriff der Makromodelle die Anzahlen von Individuen einer bestimmten Kategorie, beispielsweise einer gewissen Altersklasse, erfaBt.

2. Endliche stochastische Automaten 2 2. 1. Definition eines SEZAPO 2 2. 2. Interpretation ur. d Ablauf 3 2. 3. Assoziierte stochastische Prozesse 3 2. 4. Bemerkungen zur Automatendefinition 5 2. 5. Hilfssatze 6 2. 6. Einfach stationarer Input 7 2. 7. Verwandte Definitionen stochastischer Automaten 9 2. 8. Markovprozesse bei einfachem Input 10 2. 9. Sequentialstatistiken 12 2. 10. Spezielle Typen stochastischer Automaten 13 2. 11. Gekoppelte stochastische Automaten 15 3. Zufallige Verteilungen und Verteilungsautomaten 17 3. 1. Die Zustandsverteilung als zufalliger Vektor 17 3. 2. Momente und charakteristische Funktion der Zustandsverteilung; 21 _n 3. 3. Verteilungsautomaten 23 4. Grenzwertsatze ftir endliche regulare stochastische Automaten 28 4. 1. Satze tiber den ZustandsprozeE 29 4. 2. Satze tiber Output- und InputprozeE 31 5. Anwendung stochastischer Automaten in der Lerntheorie 36 5. 1. Das Reizstichproben-Modell von ESTES 37 5. 1. 1. Axiome des (N,2)-Patternmodells 37 5. 1. 2. Interpretation als SEZAPO 38 5. 1. 3. Grenzverhalten 41 5. 1. 4. Nichtkontingente Verstarkungsvorschrift 42 5. 1. 5. Anwendung der Grenzwertsatze 44 5. 2. Das lineare Lernmodell von BUSH und MOSTELLER 47 v 6. Automatenmodelle sequentieller Spiele 48 6. 1. Beschreibung der Spielsituation 48 6. 2. Ein probabilistisches Gefangenendilemma 49 6. 3. Interpretation als Koppelprodukt 51 6. 4. Ausblick 52 7. Ein Stimulus-Sampling-Modell mit adaptiven Transitionswahrscheinlichkeiten 55 7. 1. Einftihrung 55 7. 2. Stochastische Automaten mit variabler Struktur 57 7. 3. Anwendungen auf das (N,2)-Modell 59 Literaturverzeichnis 64 66 Zustandsgraph des (N,2)-Inputautomaten 1.