2007, Henrion, René, Küchler, Christian, Römisch, Werner

Polyhedral discrepancies are relevant for the quantitative stability of mixed-integer two-stage and chance constrained stochastic programs. We study the problem of optimal scenario reduction for a discrete probability distribution with respect to certain polyhedral discrepancies and develop algorithms for determining the optimally reduced distribution approximately. Encouraging numerical experience for optimal scenario reduction is provided.

2006, Henrion, René, Küchler, Christian, Römisch, Werner

Discrete approximations to chance constraints and mixed-integertwo-stage stochastic programs require moderately sized scenario sets. The relevant distances of (multivariate) probability distributions for deriving quantitative stability results for such stochastic programs are B-discrepancies, where the class B of Borel sets depends on their structural properties. Hence, the optimal scenario reduction problem for such models is stated with respect to B-discrepancies. In this paper, upper and lower bounds, and some explicit solutions for optimal scenario reduction problems are derived. In addition, we develop heuristic algorithms for determining nearly optimally reduced probability measures, discuss the case of the cell discrepancy (or Kolmogorov metric) in some detail and provide some numerical experience.