Automatica, February, 1998, Volume 34, No. 2


A New Editorial Appointment

Beginning January 1, 1998, Prof. Alain Haurie of the University of Geneva was appointed Editor of AUTOMATICA. He assumes the title of Editor for Management and Decision Sciences and succeeds Christine Mitchell, who resigned because of pressure of other work. I am most pleased to welcome Prof. Haurie to the Editorial Board.

After the brief biographical sketch that follows this introduction Prof. Haurie describes his view of the place of his editorial area in the systems and control field. I warmly endorse his invitation for innovative contributions on applications of management and decision sciences to the wide variety of planning under uncertainty problems that arise in environmental, economic and management systems.

Huibert Kwakernaak
Editor-in-Chief, Automatica

Alain B. Haurie, AUTOMATICA Editor for Management and Decision Sciences

Alain B. Haurie graduated in Mathematics (University of Algiers, 1961). He undertook graduate studies in Theoretical Physics (University of Algiers, Algeria, 1962) and Applied Mathematics (University of Paris-6, 1969-1970). He obtained a "doctorat de 3-éme cycle'' in Applied Mathematics (University of Paris-6, 1970) and a "doctorat d'état" in Physics (University Paris-7, 1976). His thesis topic was Jeux coopératifs, suivi de commande optimale sur un horizon infini.

He began his academic career in Algiers, as an assistant in Theoretical Physics (1961-1962). Then he joined the University of Grenoble, France (1962). In 1963 he moved to the École des Hautes Études Commerciales, Montréal, Canada, where he has been Professor of Quantitative Methods (assistant and full) from 1963 to 1989. Since 1989 he has been Professor of Operations Research at the Faculty of Economics and Social Sciences, University of Geneva, Switzerland.

During his career, he has been chairman of department (HEC-Montréal 1974-1976, University of Geneva, 1989-1992), and director of a research group (GERAD, HEC-Montréal, 1980-1989). In addition to his normal assignment he has taught in various programs and institutions (École Polytechnique de Montréal. 1970-1974, INSEAD, Rabat, Morocco, University of California, Berkeley, USA, 1980, Victoria University, Wellington, New-Zealand, 1993, and École des Mines de Nantes, France, 1993-1995.

Prof. Haurie is Fellow of the Royal Society of Canada, Academy of Humanities and Social Sciences, President of the International Society of Dynamic Games, Associate Editor of Discrete Event Systems: Theory and Applications, Associate Editor of Environmental Modeling & Assessment, former Associate Editor of the IEEE Transaction on Automatic Control (1988--1991), and Associate Editor of the Journal of Economic Dynamics and Control.

Management and Decision Sciences, Challenge and Opportunities for Control and Optimization Applications

Alain B. Haurie
Department of Management Studies, University of Geneva, Geneva, Switzerland

In these pages I intend to illustrate the different components of the area Management and Decision Sciences that I will be in charge of, as an area editor, for the coming years. To do so I will rely mostly on some research topics I know well for having contributed a little myself to their development. This area is very wide but I see several conducting lines through this variety of domains that are all related with the use of control and optimization paradigms both for modeling and computation/simulation purposes.

Large scale systems: The definition of what is a large scale system is constantly "moving to the right" on the dimension scale. This is due to the considerable progresses of processors and parallel machines but also to revolutionary development in algorithms. Quoting from the preface of the recent book of Roos, Terlaky and Vial on linear optimization [35]

For example, linear models of airline crew scheduling with as many as 13 million variables have recently been solved within 3 minutes on a four processor Silicon Graphics Power Challenge workstation.

The revolution in convex optimization algorithms was initiated by Khachiyan [25] in 1979 when he proposed the ellipsoid method for linear optimization, the first polynomial-time algorithm for linear programming. Shortly after, in 1984, Karmarkar produced the first efficient interior point algorithm [23]. Applying these ideas gave rise to a new generation of commercial codes for LP (Linear programming), LCP (Linear complementarity problems) and QP (Quadratic programmin) that beat former codes by several orders of magnitude. Nesterov and Nemirovski [31] generalized the field to nonlinear convex optimization (structural programming) with an interesting outreach, called Semidefinite Optimization (SDO) that proved to be well adapted to the treatment of notoriously difficult problems in system theory as shown in the survey of Boyd and Vanderberghe [5]. Amazingly enough, SDO also contributes to important progresses in the area of combinatorial optimization (see e.g.[16, 17].) As a consequence, researchers from different horizons, management science, system theory, combinatorics share the same set of theoretical tools and benefit from an important potential of cross fertilization.

Operational research applications of control and optimization: What is called Stochastic control in system theory has developed under the name of Markov decision processes (MDP) [32]or Stochastic programming [24] in operational research. The underlying technique is in all cases related to dynamic programming. Here again, after a long parallel development the two fields are cross fertilizing. Indeed, as demonstrated magistrally in [28] the numerical solution of control problems for stochastic jump and diffusion processes uses an approximation via MDPs. The solution of MDPs means a fixed-point search for a local transition reward operator. This is almost always a large scale problem. There is a unifying paradigm linking linear programming and policy iteration in MDPs which can benefit a lot from the recent advances in linear optimization algorithms. Singular perturbations of stochastic systems [27], a classic field in system theory, when extended to MDPs [12] yield an interesting example of LP decomposition à la Dantzig-Wolfe [11] that can itself be implemented in an efficient way, through the use of interior point methods (see [1, 2, 15, 18] for a brief tour of this domain.) As another example of cross fertilization let's consider the area of stochastic programming. Here the initial formulation dates back from the early days of linear programming [11]. The field did not develop for some time because of the curse of dimensionality. Then stochastic programming as well as dynamic programming benefited a lot from the progresses in nonsmooth analysis [10] exemplified in the work of King, Rockafellar and Wets [34, 26]. The domain is now in full development with the implementation of advanced codes based on a combination of large scale optimization and importance sampling (see e. g. [22, 21].)

Environmental management: Environmental management is an interdisciplinary business. Natural sciences, economics, management, sociology all concur in bringing an understanding of the complex interactions between human activities and the environment. A recent book [9] gives a set of examples of the possible contributions of OR and control theoretic modeling techniques to environmental management. Stochastic programming [14], large scale linear optimization models, stochastic linear system analysis [6, 13] have already been used with success in environmental modeling. Typically an environmental management problem involves a natural medium like an airshed, a river basin, the soil where a pollutant is emitted and then dispersed and deposited. This dispersion process is usually described as a distributed parameter dynamical system. Dispersion models for air pollutants like ozone require super computers for their numerical solutions. In the linking of these dispersion models with models of emission rates due to economic activity one has to deal with a multiplicity of time scales (minutes for dispersion, years for investment decisions, decades for global environmental change assessment) and a lot of uncertainty. On top of that, environmental management involves usually a conflict resolution process as several interest groups compete for the same limited natural resource. I may refer to [20] for an example of an environmental management model encompassing these different aspects.

Economic dynamics: The calculus of variations and its modern development, the maximum principle, have provided economic theory with a set of powerful paradigms to analyze intertemporal choices. The economic models have motivated, in particular, a series of original developments concerning asymptotic control [8]. The potential contributions of control theory (both deterministic or stochastic) and differential game theory (again both deterministic and stochastic) are still very important in all aspects of dynamic economic theory and more particularly in the field called industrial organization.

Business and management techniques: The Nobel Prize in economics has been attributed this year to Scholes and Merton [7, 29] for their work on option pricing. The recent book of Musiela and M. Rutkowski [30] is an up to date reference about the dynamic modeling of financial markets. Risk management is also omnipresent in all facets of management and there is no doubt that stochastic or robust control techniques can help in this regard.

Decision support systems: Modern desk top computers allow powerful computations and integration between different types of software and applications. Decision support systems in environmental management can integrate a dynamical system simulation module for air pollution dispersion with a geographical information system socio-economic data base locating the emission sources and the population risk exposure (see e.g. the web site

for a presentation of such an integrated DSS.) The potential contribution of control and dynamical system optimization in integrated DSSs is considerable.

Conflict resolution: Finally, in socio-economic problems the multiplicity of actors and criteria calls for the definition of conflict resolution paradigms. Negotiation, bargaining, coalition building, equilibria based on threats are concepts that entail a dynamical background. This is a subdomain of the theory of cooperative games where dynamical system theory should also contribute intensively.

Such a brief flight over so wide an area will probably leave many readers unsatisfied because a particular important topic has been left aside. This list is certainly not exhaustive, just a review of some themes this area editor is more directly concerned with. It is the responsibility of those who develop new methods and techniques for grasping the complexity of dymamic management problems to bring them to the fore by publishing fine papers in international journals like Automatica. This journal is indeed the perfect forum for fostering the exchange of high level research ideas bridging the different fields in the area of management and decision sciences. This journal welcomes innovative contributions in these fields with applications to the wide variety of planning under uncertainty problems that arise in environmental, economic and management sciences.

[1] Abbad, M. and J. A. Filar (1992), "Perturbation and Stability Theory for Markov Control Problems,'' IEEE Transactions on Automatic Control, Vol. AC-37, 9, pp. 1415-1420.

[2] Abbad, M. and J. A. Filar (1992), "Algorithms for Singularly Perturbed Limiting Average Markov Control Problems,'' IEEE Transactions on Automatic Control, Vol. AC-37, 9, pp. 1421-1425, 153-168.

[3] Basar, T. and G. J. Olsder (1982), Dynamic Noncooperative Game Theory, Academic Press, London/New York.

[4] Bielecki, T. R. and J. A. Filar (1991), "Singularly Perturbed Markov Control Problems,'' Annals of Operations Research, Vol. 29, pp. 153-168.

[5] Boyd, S. E. and Vandenberghe (1996), ``Semidefinite programming,'' SIAM Review, Vol. 38, 1, pp. 49-96.

[6] Braddock, R. D., J. A. Filar, R. Zapert, M. G. den Elzen and J. Rotmans (1994), "Mathematical formulation of the IMAGE greenhouse effect model,'' Applied Mathematical Modelling, Vol. 18, pp. 234-254.

[7] Black, F. and M. Scholes (1973), "The pricing of options and corporate liabilities,'' Journal of Political Economy, Vol.81, May-June, pp. 637-654.

[8] Carlson, D. A., A. Haurie and A. Leizarowitz (1991), Infinite Horizon Optimal Control: Deterministic and Stochastic Systems, Springer Verlag, New York.

[9] Carraro, C. and A. Haurie, eds. (1996), Operations Research and Environmental management, Kluwer, The Netherlands.

[10] Clarke, F. (1983), Optimization and Nonsmooth Analysis, J. Wiley & Sons, New York.

[11] Dantzig, G. B. (1963), Linear Programming, Princeton Univ. Press, Princeton, New Jersey.

[12] Delebecque, F. and J.-P. Quadrat (1981), "Optimal Control of Markov Chains Admitting Strong and Weak Interactions, Automatica, Vol 17, pp. 281-296.

[13] Filar, J. A. and R. Zapert (1996), "Uncertainty analysis of a greenhouse effect model,'' pp. 101-118, in C. Carraro and A. Haurie, eds., Operations Research and Environmental Management, Kluwer, The Netherlands.

[14] Fragniére, E. and A. Haurie (1996), "MARKAL-Geneva, a model to assess energy-environment choices for a Swiss canton,'' pp. 41-68, in C. Carraro and A. Haurie eds., Operations Research and Environmental Management, Kluwer, The Netherlands.

[15] Filar, J.-A. and A. Haurie (1997), "Optimal ergodic control of singularly perturbed hybrid stochastic systems,'' in G. G. Yin and Q. Zhang eds. Mathematics of Stochastic Manufacturing Systems, Lectures in Applied Mathematics, Vol. 33, American Mathematical Society, Providence, RI, USA.

[16] Goemans, M. X. (1997), "Semidefinite programming in combinatorial optimization,'' Mathematical Programming, Vol. 79, pp. 143-161.

[17] Goemans, M. X. and D. P. Williamson (1995), "Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming,'' J. ACM, Vol. 42, pp. 1115-1145.

[18] Goffin, J.-L., A. Haurie and J.-P. Vial (1992), "Decomposition and nondifferentiable optimization with the projective algorithm,'' Management Science, Vol. 38, 2, pp. 284-302.

[19] Goffin, J.-L., A. Haurie, J.-Ph. Vial and D.L. Zhu (1993), "Using Central Prices in the Decomposition of Linear Programs,'' European Journal of Operational Research, Vol. 64, pp. 393-409.

[20] Haurie, A. and J. Krawczyk (1997), "Optimal charges of agents in a river basin with lumped and distributed emissions,'' Environmental Modelling and Assessment.

[21] Higle, J. L. and S. Sen (1996), Stochastic Decomposition, Kluwer Academic Publishers, Dordrecht.

[22] Infanger, G. (1994), Planning under Uncertainty, The Scientific Press Series, Denver.

[23] Kall, P. and S. W. Wallace (1994), Stochastic Programming, John Wiley and Sons, Chichester.

[24] Karmarkar, N. K. (1984), "A new polynomial-time algorithm for linear programming,'' Combinatorica, Vol. 4, pp. 373-395.

[25] Khachian, L. G. (1979), "A polynomial algorithm in linear programming,'' Doklady Akademiia Nauk SSSR, Vol. 244, pp. 1093-1096.

[26] King, A. and T. Rockafellar (1993), "Asymptotic theory for solutions in statistical estimation and stochastic programming,'' Mathematics of Operations Research, Vol. 18, pp. 148-162.

[27] Kushner, H. J. (1990), Weak Convergence Methods and Singularly Perturbed Stochastic Control and Filtering Problems, Birkhäuser, Boston.

[28] Kushner, H. J. and P. Dupuis (1995), Numerical Methods for Stochastic Control Problems in Continuous Time, Springer Verlag, Berlin/N.Y.

[29] Merton, R. C. (1990), Continuous-Time Finance, Blackwell, Cambridge USA.

[30] Musiela, M. and M. Rutkowski (1997), Martingale Methods in Financial Modelling, Springer-Verlag.

[31] Nesterov, Y. E. and A. S. Nemirovski (1993), Interior Point Polynomial Methods in Convex Programming: Theory and Algorithms, SIAM Publications, Philadelphia.

[32] Puterman, M. (1994) Markov Decision Processes, J. Wiley & Sons.

[33] Ramsey, F. (1928), "A Mathematical Theory of Savings,'' Economic Journal, Vol. 38, pp. 543-549.

[34] Rockafellar, R. T. and J.-B. Wets (1991), "Scenarios and Policy Aggregation in Optimization under Uncertainty,'' Mathematics of Operations Research, Vol. 16, pp. 119-147.

[35] Roos, C., T. Terlaky and J.-P. Vial (1997), Theory and Algorithms for Linear Optimization, J. Wiley, New York.

[36] Ruszczynski, A. (1997), "Decomposition methods in stochastic programming,'' Mathematical Programming, Vol. 79, pp. 333-353.

Last modified on November 23, 1997