Stochastic multi-stage linear programs are rarely used in practical applica
tions due to their size and complexity. Using a general matrix to aggregate
the constraints of the deterministic equivalent yields a lower bound. A si
milar aggregation in the dual space provides an upper bound on the optimal
value of the given stochastic program. Jensen's inequality and other approx
imations based on aggregation are a special case of the suggested approach.
The lower and upper bounds are tightened by updating the aggregating weigh
ts. (C) 1999 Elsevier Science B.V. All rights reserved.