A Scalable Bounding Method for Multi-Stage Stochastic Integer Programs

Abstract

Many dynamic decision problems involving uncertainty can be appropriately modeled as multi-stage stochastic programs. However, most practical instances are so large and/or complex that it is impossible to solve them on a single computer, especially due to memory limitations. Extending the work of Sandikci et al. (2013) on two-stage stochastic mixed-integer-programs (SMIPs), this paper develops a bounding method for general multi-stage SMIPs that is based on scenario decomposition. This method is broadly applicable, as it does not assume any problem structure including convexity. Moreover, it naturally fits into a distributed computing environment, which can address truly large-scale instances. Extensive computational experiments with large-scale instances (with up to 40 million scenarios, 5.2 × 108 binary variables and 3.3 × 108 constraints) demonstrate that the proposed method scales nicely with problem size and has immense potential to obtain high quality solutions to practical instances within a reasonable time frame.

Keywords: Stochastic programming, Multi-stage, Mixed-integer variables, Bounding, Parallel computing