American Institute of Mathematical Sciences

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April  2008, 4(2): 363-384. doi: 10.3934/jimo.2008.4.363

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

René Henrion 1, , Christian Küchler 2, and  Werner Römisch 2,

1. 

Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany
2. 

Humboldt-Universität zu Berlin, Institut für Mathematik, 10099 Berlin, Germany, Germany

Received  July 2007 Revised  February 2008 Published  April 2008

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.
Keywords: Kolmogorov metric., chance constraints, scenario reduction, discrepancy, two-stage, Stochastic programming, mixed-integer.
Mathematics Subject Classification: Primary: 90C1.
Citation: René Henrion, Christian Küchler, Werner Römisch. Discrepancy distances and scenario reduction in two-stage stochastic mixed-integer programming. Journal of Industrial and Management Optimization, 2008, 4 (2) : 363-384. doi: 10.3934/jimo.2008.4.363
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