Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

René Henrion; Christian Küchler; Werner Römisch

doi:10.3934/jimo.2008.4.363

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2008, Volume 4, Issue 2: 363-384. Doi: 10.3934/jimo.2008.4.363

This issue Previous Article A filled function method for constrained nonlinear integer programming Next Article Higher-order symmetric duality in multiobjective programming with invexity

Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming

1.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin
2.
Humboldt-Universität zu Berlin, Institut für Mathematik, 10099 Berlin

Received: June 30, 2007

Revised: January 31, 2008

Published: March 2008

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C15.

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