Solution of Large Scale Stochastic Programs with Stochastic Decomposition Algorithms

Stochastic Decomposition (SD) is a randomized version of Benders’ decomposition for the solution of two stage stochastic linear programs with recourse. It combines a recursive sampling scheme within a decomposition-coordination framework in which the algorithm alternates between a master program and. a subprogram. The master program represents a piecewise linear approximation in which each cut is obtained by solving one linear subproblem, and then performing a series of updates based on previously generated outcomes. Using recursive updates, we devise an efficient computer implementation that allows us to address very large two stage stochastic programs with recourse. We report our computational experience with some very large stochastic programs that arise in aircraft fleet scheduling and telecommunications network planning.