Stochastic Integer Programming: Limit Theorems and Confidence Intervals

Authors:
Andreas Eichhorn;Werner Römisch
Affiliations:
Department of Mathematics, Humboldt-University Berlin, Unter den Linden 6, 10099 Berlin, Germany;Department of Mathematics, Humboldt-University Berlin, Unter den Linden 6, 10099 Berlin, Germany
Venue:
Mathematics of Operations Research
Year:
2007

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Abstract

We consider empirical approximations (sample average approximations) of two-stage stochastic mixed-integer linear programs and derive central limit theorems for the objectives and optimal values. The limit theorems are based on empirical process theory and the functional delta method. We also show how these limit theorems can be used to derive confidence intervals for optimal values via resampling methods (bootstrap, subsampling).