Improving aggregation bounds for two-stage stochastic programs

Authors:
Charles H. Rosa;Samer Takriti
Affiliations:
SABRE Decision Technologies, One East Kirkwood Boulevard, MD 7390, Southlake, TX 76092, USA;Mathematical Sciences Department, IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
Venue:
Operations Research Letters
Year:
1999

Citing 5
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Abstract

Stochastic multi-stage linear programs are rarely used in practical applications due to their size and complexity. Using a general matrix to aggregate the constraints of the deterministic equivalent yields a lower bound. A similar aggregation in the dual space provides an upper bound on the optimal value of the given stochastic program. Jensen's inequality and other approximations based on aggregation are a special case of the suggested approach. The lower and upper bounds are tightened by updating the aggregating weights.