Stochastic programming with integer variables

Stochastic programming with integer variables

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Article ID: iaor20041837
Country: Germany
Volume: 97
Issue: 1/2
Start Page Number: 285
End Page Number: 309
Publication Date: Jan 2003
Journal: Mathematical Programming
Authors:
Keywords: programming: integer
Abstract:

Including integer variables into traditional stochastic linear programs has considerable implications for structural analysis and algorithm design. Starting from mean-risk approaches with different risk measures we identify corresponding two- and multi-stage stochastic integer programs that are large-scale block-structured mixed-integer linear programs if the underlying probability distributions are discrete. We highlight the role of mixed-integer value functions for structure and stability of stochastic integer programs. When applied to the block structures in stochastic integer programming, well known algorithmic principles such as branch-and-bound, Lagrangian relaxation, or cutting plane methods open up new directions of research. We review existing results in the field and indicate departure points for their extension.

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