Ann Oper Res (2011) 186:83–99 DOI 10.1007/s10479-009-0602-8 Testing successive regression approximations by large-scale two-stage problems István Deák Published online: 18 September 2009 © Springer Science+Business Media, LLC 2009 Abstract A heuristic procedure, called successive regression approximations (SRA) has been developed for solving stochastic programming problems. They range from equation solving to probabilistic constrained and two-stage models through a combined model of Prékopa. We show here, that due to enhancements in the computer program, SRA can be used to solve large-scale two-stage problems with 100 first stage decision variables and a 120 dimensional normally distributed random right hand side vector in the second stage problem. A FORTRAN source program and computational results for 124 problems are presented at www.uni-corvinus.hu/~ideak1. 1 Introduction Stochastic programming problems frequently have functions that can not be evaluated accu- rately (expected recourse or probabilities of some events e.g.)—but they can be computed by some Monte Carlo integration technique (with some sampling error). The successive regres- sion approximations method is based on the idea of replacing the numerically hard functions by an ever-improving regression function. We solved the following types of problems by this technique: equation solving (Deák 2001a, 2001b), stochastic programming problems with probabilistic constraint (Deák 2003), two-stage problems (Deák 2002b, 2006), and a com- bined model of Prékopa (Deák 2003) (for the model see Prékopa 1995, p. 417–418). In Sect. 2 we give a short overview of the Successive Regression Approximations (SRA) technique as applied to the two-stage problem (Deák 2002b, 2003, 2006). This SRA method is heuristic, no theoretical proof exists that the author is aware of, but the computational results presented here indicate, that this method is promising. The troublesome expected recourse function is supposed to have only estimated values (noisy function values), and Research supported by National Scientific Research Fund (Hungary), grant T047340. I. Deák ( ) Computer Science Department, Corvinus University of Budapest, Fovam ter. 8., 1093 Budapest, Hungary e-mail: istvan.deak@uni-corvinus.hu