Simulation-based confidence bounds for two-stage stochastic programs

This paper provides a rigorous asymptotic analysis and justification of upper and lower confidence bounds proposed by Dantzig and Infanger (1995) for an iterative sampling-based decomposition algorithm, introduced by Dantzig and Glynn (1990) and Infanger (1992), for solving two-stage stochastic programs. Extensions of the theory to cover use of variance reduction, different iterative sampling sizes, and the dropping of cuts are also presented. An extensive empirical investigation of the performance of these bounds establishes that the bounds perform reasonably on realistic problems. ∗Technical Report SOL 2008-1.