Planning Under Uncertainty: Solving Large-Scale Stochastic Linear Programs (The Scientific Press Series)

Planning Under Uncertainty: Solving Large-Scale Stochastic Linear Programs presents a new approach devised by George Dantzig, P. Glynn, and Gerd Infanger. This approach makes it possible to solve large-scale stochastic linear problems with numerous stochastic parameters. Although efficient technologies have been developed to solve large deterministic dynamic linear systems, deterministic methodologies cannot account for real-world uncertainties. Stochastic models avoid this shortcoming but are often computationally expensive or intractable. The method explained in this book has been successfully tested on facility expansion and financial planning problems. In one case, a problem whose deterministic equivalent would appear as a linear programming problem with approximately 1,027 constraints and variables was solved on a laptop 80386 computer. In this monograph, Gerd Infanger shows how large-scale stochastic linear problems can be solved efficiently by combining classical decomposition and Monte Carlo (importance) sampling techniques. The author discusses the methodology for solving two-stage stochastic linear programs with recourse and presents numerical results of large problems with numerous stochastic parameters. He shows how to efficiently implement the methodology on a parallel multicomputer and derives the theory for solving a general class of multistage problems with dependency of the stochastic parameters within a stage and between different stages.