Column Generation within the L-shaped Method for Stochastic Linear Programs

We develop a method that incorporates column generation within the Lshaped method for solving two-stage stochastic linear programs. This method adds feasibility and optimality cuts generated from the second-stage subproblems based on the current columns in the master problem of the L-shaped method. It also generates columns for the master problem with respect to the first-stage constraints as well as existing feasibility and optimality cuts. We present different algorithmic strategies and prove finite convergence for a wide variety of approaches. We explore the performance of various algorithm designs that employ stabilization subroutines for strengthening both column and cut generation to effectively avoid degeneracy. To demonstrate the computational performances of the algorithmic approaches, we study a two-stage stochastic version of the cutting stock problem.