50 Years of OR

50 Years of Operations Research at TU Wien

The 50th anniversary of Operations Research (OR) at TU Wien was marked by a special lecture, (pptx download) delivered by Richard Hartl, and gathering of some of the leading figures in its history. Here we reflect on the turning points and key figures who have shaped and sustained its development over half a century.

What is Operations Research?

Operations research Operations research (OR) is the area of Applied Mathematics devoted to decision-making. This is almost always done by optimizing some criterium (or several criteria, in a Pareto sense), and tightly relates to Optimization theory. Characterizing extreme values and designing efficient algorithms to approximate them is particularly relevant. The corresponding study of iterative schemes often connects with (discrete or continuous) Dynamics (D).

OR at TU Wien

Some early OR problems were considered in the Mathematical Institute of the Technische Hochschule Wien (TH Wien) in the middle of the fifties, an innovation  which was closely linked to the introduction and subsequent development computers. One of the earliest applications, attributed to W. Knödel, related to a transportation problem arising in the Austrian sugar industry.

The growing importance of mathematical methods in planning problems led to the foundation of the Institut für Unternehmensforschung in 1972 (“Unternehmensforschung” acted as the German translation of OR at that time, but was soon changed to “Operations Research”). Generally, the late sixties and seventies showed a remarkable increase in the number of institutes and researchers at the universities in Austria (and elsewhere) engaged in informatics, economics and business administration.

The Institut für Unternehmensforschung was established within the Faculty of Mathematics. The newly founded institute was small: one full professor, Gustav Feichtinger, one assistant, Alexander Mehlmann, and one secretary, Sylvia Puhl until 1973, then Maria Toda. The institute offered a two-semester course on OR-methods, 4 hours per week each as well as special courses on various topics of optimization, decision theory, queueing models, reliability and maintenance among other OR topics.  In the period from 1973 to 1974, two additional assistants were hired, namely Mikulas Luptacik and Judith Rosenfeld, and subsequently Richard F. Hartl, who will present the celebratory lecture to mark 50 years in October 2022.

Among the research issues at this early stage were manpower planning, population dynamics, mathematical (particularly geometric) programming and various applications of dynamic optimization.

Evolution  of  ORDYS

Since the late seventies, optimal control (OC) theory and its applications to intertemporal decision-making were one of the key  research areas of the institute.  Inherent nonlinearities of such decision problems often lead to complex solutions such as multiple equilibria, history-dependence and limit cycles.

One main goal of ORDYS (“Operations Research and Dynamical Systems”) was the study of economic mechanisms behind these complexities. To get insights into the qualitative structure of complex optimal solutions, bifurcation theory was used. In the eighties and nineties, ORDYS was among the first research groups applying bifurcation results to nonlinear dynamic OR-models. This innovative way led to new results  on the solution paths, particularly on their oscillatory and chaotic behavior.

Among further early methodological research issues of ORDYS were a correct treatment of pure path constraints, the study of the optimal mix of the control instruments, and a complete analysis of SKIBA points (manifolds),particularly in the context of concavites.

An important instrument for the numerical analysis of OC problems is the toolbox OCMat  developed by D. Grass and successively improved during the last two decades.

A further field were multi-stage optimal control methods, where a decision-maker not only has continuous control instruments available, but also the choice to adopt a different regime which differs with respect to the system dynamics and/or the objective at an optimally determined point in time. Noteworthy applications have been obtained by A, Seidl.

Another research topic of ORDYS (and later of ORCOS) were age-structured OC models  arising in vintage capital accumulation and manpower planning. Their analysis required known distributed parameter control optimality conditions and its extensions derived by V. Veliov.

Real-world decision processes often involve more than one decision-maker.  Taking into account the dynamic competitive (or cooperative) interaction of the players leads us to the field of Differential Games (DGs). The contributions of A. Mehlmann, H. Dawid and others should be mentioned in that context.

OC and DG methods are relevant for the following applications investigated at the research unit. In the seventies, the group started analyzing  the Dynamics of the firm, where virtually all areas of business activities of a firm such as production & inventory, investment, marketing, environmental planning etc. are analyzed in an OC-framework. Cooperating with the ’Dutch School of Firm Dynamics’ (mostly with P. M. Kort), the group was particularly successful with the ‘path-coupling’ method. In  the  ‘red bible’ by Feichtinger and Hartl (1986) some of the results obtained at that time are summarized.

In the nineties, the interest focused in OR applications of Public Policy Making. An important field dominating the research agenda for several years was the Economics of crime, or more general, the Economics of ‘deviant’ behavior. Among them are corruption, the dynamics and control of illicit drugs (particularly the US-American cocaine epidemics which was investigated by J. Caulkins, G. Tragler and D. Behrens), where the optimal mix of law enforcement, treatment and prevention is crucial, terror and efficient counter-terror measures (e.g. a differential game extension of E. Kaplan’s terror queueing model as well as a 3-D extension of the Lanchester scenario in form of so-called ‘truels’). In the ‘yellow bible’ most of these unorthodox applications  are collected (Grass et al. 2008).

Following the work of Nobel Laureate G.S Becker, E. Dockner and others studied habit formation and addiction. In particular, they identified mechanisms leading to stable persistent oscillations in consumption, e.g. so-called ‘binge drinking’.

Researchers at ORDYS

Christian Almeder, Doris Behrens, Herbert Dawid, Maria Dworak, Engelbert Dockner, Thomas Fent, C. Gavrila, Dieter Grass, Alfred Kalliauer, Michael Kopel, Alexandra Milik, Andreas Novak, Alexia Prskawetz, Andrea Seidl, Gerhard Sorger, Alois Steindl, Harald Vogelsang, Franz Wirl, Stefan Wrzaczek, Yuri Yegorov, Georges Zaccour, Irmgard Zeiler.

Cooperation Partners

Raouf Boucekkine, Jonathan P. Caulkins,  Christophe Deissenberg, Fouad El’Ouardighi, Cars Hommes, Steffen Jörgensen, Ed H. Kaplan, Peter M. Kort, Moshe Kress, George Leitmann, Alfred Luhmer, Sergio Rinaldi, Warren Sanderson, Willi Semmler, Suresh P. Sethi.

Evolution of ORCOS

The research unit „Operations Research and Control Systems” (ORCOS) became the successor of ORDYS, after the retirement of Prof. Feichtinger in 2008 and the appointment of V. Veliov as head of the unit. Applications of Optimal Control with a focus on economics, demography and social sciences were central for ORDYS and they remained as areas of intensive work of ORCOS. In parallel, more attention was attributed to the further development of various theoretical aspects related to optimization and optimal control, and the pertaining numerical analysis. This applies to problems with discrete dynamics and such described by ordinary or partial differential equations (ODE or PDE).

As is usual in optimization, the necessary optimality conditions in optimal control have the form of a differential variational inequality. Many properties related to optimal control problems can be more generally formulated and studied in terms of variational inequalities. Therefore, the investigation of various regularity properties of variational inequalities in general or specific Banach spaces constituted an important part of the research of ORCOS. This led to new results on convergence and error analysis of discretization and numerical methods for optimal control and more general optimization problems. The Model Predictive Control method was an important specialized subject. Particular emphasis in the investigations was given to affine optimal control problems for ODE or PDE systems, for which the notion of bi-metric regularity was introduced and investigated. In addition, ORCOS substantially contributed to the theory of Infinite horizon control problems. Inherited from ORDYS, the novel contributions to the theory of heterogeneous systems (age- or size-structured systems, or other systems with continuum of agents) created a base for numerous control applications.

In alignment with the above, ORCOS carried out application-oriented research in various areas outlined below.

Electricity market problems

— smart grid business models including batteries; demand response market

— electricity production and storage; energy option pricing

Epidemiology:

— incorporating heterogeneity in dynamic (and control) models: age, risky behavior, infection age, immunity;

— epidemiological and economic consequences of anti-epidemic policies: lock-down, social distancing, vaccination, testing

Environment and economics:

— trading with emission permits;

— global warming

— optimal harvesting and optimal cyclic exploitation of renewable resources

— control of pollution and environmental absorption capacity; optimal pollution policies in lakes

— optimal paths for renewable energy production

— pollution/production trade-off

Demography and economics:

— health economics: life cycle optimization models including investments in health and insurance

— optimal education policies and development of human capital; education and population growth

— optimal election policies in organizations;

— optimal immigration polices

Social sciences:

— addiction phenomena: optimal prevention, law enforcement and treatment

— investment in skills: art, sport, science

The size of ORCOS varied during the years between 8 and 14 employees. The TU-staff included Gustav Feichtinger (Prof. emeritus), Josef Haunschmied, Raimund Kovacevic, Gernot Tragler, Vladimir Veliov, and Margit Kainerstorfer (secretary).

ORCOS had externally financed projects (FWF, FFG, EU) for more than 2.5 Million Euro. This allowed to appoint project assistants at predoc or postdoc level:

Angelov, A. Belyakov, A.D. Corella ,   K. Frank,  D. Grass,  T. Hanh,  V. Lykina,  E. Moser,  C. Simon,  A. Seidl,  B. Skritek,  V.N. Vinh,  P.T. Vuong ,  A. Widder,  S. Wrzaczek

In the 14 years of its existence, ORCOS edited or co-edited 9 books, published over 200 (??) papers in scientific journals and above 40 in books and proceedings.

The Operations Research unit at TU Wien existed under the name ORCOS till the retirement of Prof. Veliov in 2022.

ORCOS to VADOR

In October 2021, Prof. Aris Daniilidis took up his position as head of the research department, which is renamed VADOR – Variational Analysis, Dynamics and Operations Research.  This reflects his specific research interests, while still embracing the key pillars of ORCOS – control theory, dynamics and OR (pdf).

Workshops, Conferences and Collaborations

In 1978, members of the institute were involved in the foundation and subsequent development of the Austrian Society for Operations Research (ÖGOR) in 1978.

From 1980, the institute organized a series of international OR-conferences, in particular several joint Austrian-German-Swiss OR meetings.  A highlight was certainly the 1990 meeting of the DGOR, GMOEOR, SVOR, and ÖGOR in Vienna, just after the fall of the Iron Curtain, which attracted more than 1200 participants, many from Eastern European countries. Institute staff were co-organisers of The Sixth European Conference of OR Societies (EURO VI), which took place at the Vienna University of Technology in 1983.

An increasing interest in dynamic games lead to the organisation of a series of international workshops on Optimal Control, Dynamic Games and Nonlinear Dynamical Systems, the first of which took place in Vienna in October 1981.  By the 14th iteration in 2015 it was decided that, because of its scale, the workshop had evolved into a conference.  The 15th Viennese Conference: Optimal Control and Dynamic Games [insert link to VC history] took place in July 2022, after a Corona imposed delay.