zbMATH — the first resource for mathematics

Stochastic programming with integer variables. (English) Zbl 1035.90053
Summary: 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.

90C15 Stochastic programming
90C11 Mixed integer programming
90C06 Large-scale problems in mathematical programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Full Text: DOI