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

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 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.*

**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

- http://ecolu-info.unige.ch/recherche/EUREKA/

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 Contro*l, 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.