A scalable bounding method for multistage stochastic programs

Many dynamic decision problems involving uncertainty can be appropriately modeled as multistage 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 [B. Sandikci, N. Kong, and A. J. Schaefer, Math. Program., 138(2013), pp. 253-272] on two-stage stochastic mixed-integer programs, this paper considers general multistage stochastic programs and develops a bounding method 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. Computational experiments with large-scale instances (with up to 100 million scenarios, about 1.5 billion decision variables-85% binary- and 800 million 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.