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: | Schultz R. |
Keywords: | programming: integer |
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.