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Abstract:

This paper introduces recent developments in the analysis of inventory systems
with partial observations. The states of these systems are typically
conditional distributions, which evolve in infinite dimensional spaces over
time. Our analysis involves introducing un-normalized probabilities to
transform nonlinear state transition equations to linear ones. With the linear
equations, the existence of the optimal feedback policies is proved for two
models where demand and inventory are partially observed. In a third model
where the current inventory is not observed but a past inventory level is
fully observed, a sufficient statistic is provided to serve as a state. The
last model serves as an example where a partially observed model has a
finite dimensional state. In that model, we also establish the optimality
of the basestock policies, hence generalizing the corresponding classical
models with full information.



Bio:
Professor Bensoussan has a long research background in stochastic control,
probability and stochastic processes. He is Professor Emeritus at the
University of Paris Dauphine. He graduated from the Ecole Polytechnique in
1962, PhD from the University of Paris in 1969. He is a member of the French
Academy of Sciences, of the French Academy of Technology, of the Academia
Europae, and of the International Academy of Astronautics. He is an IEEE
fellow; he received the Von Humboldt award, and the NASA public service medal.
Professor Alain Bensoussan had important responsibilities in the French
research system. He was President of INRIA (National Institute for Research in
Computer Science and Control) from 1984 to 1996, and President of CNES, the
French space Agency, from 1996 to 2003. He has been Chairman of the ESA
(European Space Agency) Council from 1999 to 2002. He is Officer of Legion
d'Honneur from France and Officer Bundes Verdienst Kreuz from Germany.

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