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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Received: December 2, 2002 / Accepted: April 23, 2003 Published online: May 28, 2003
Mathematics Subject Classification (2000): 90C15, 90C11, 90C06, 90C57
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Schultz, R. Stochastic programming with integer variables. Math. Program., Ser. B 97, 285–309 (2003). https://doi.org/10.1007/s10107-003-0445-z
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DOI: https://doi.org/10.1007/s10107-003-0445-z