  We consider multistage stochastic optimization problems involving multiple
units. Each unit is a (small) control system. Static constraints couple units
at each stage. We present a mix of spatial and temporal decompositions to
tackle such large scale problems. More precisely, we obtain theoretical bounds
and policies by means of two methods, depending whether the coupling
constraints are handled by prices or by resources. We study both centralized
and decentralized information structures. We report the results of numerical
experiments on the management of urban microgrids. It appears that
decomposition methods are much faster and give better results than the standard
Stochastic Dual Dynamic Programming method, both in terms of bounds and of
policy performance.
