Parallelizable Preprocessing Method for Multistage Stochastic Programming Problems

Stochastic programming has extensive applications in practical problems such as production planning and portfolio selection. Typically, the model has very large size and some techniques are often used to exploit the special structure of the programs. It has been noticed that the coefficient matrix may not be of full rank in the well-known scenario formulation of stochastic programming; thus, the preprocessing is often necessary in developing rapid decomposition methods. In this paper, we propose a parallelizable preprocessing method, which exploits effectively the structure of the formulation. Although the underlying idea is simple, the method turns out to be very useful in practice, since it may help us to select the nonanticipativity constraints efficiently. Some numerical results are reported confirming the usefulness of the method.This work was partially supported by the Informatics Research Center for Development of Knowledge Society Infrastructure, Graduate School of Informatics, Kyoto University, Kyoto, Japan. The work of the first author was also supported in part by the National Science Foundation of China, Grant 10571039. The work of the second author was also supported in part by the Scientific Research Grant-in-Aid from the Japan Society for the Promotion of Science. The authors are grateful to the referees for careful reading of the paper and helpful comments.This author’s work was done while he was visiting Kyoto University.