Traditionally, two variants of the L-shaped method based on Benders’ decomposition principle are used to solve two-stage stochastic programming problems: the aggregate and the disaggregate version. In this study we report our experiments with a special convex programming method applied to the aggregate master problem. The convex programming method is of the type that uses an oracle with on-demand accuracy. We use a special form which, when applied to two-stage stochastic programming problems, is shown to integrate the advantages of the traditional variants while avoiding their disadvantages. On a set of 105 test problems, we compare and analyze parallel implementations of regularized and unregularized versions of the algorithms. The results indicate that solution times are significantly shortened by applying the concept of on-demand accuracy. 
Applying oracles of on-demand accuracy in two-stage stochastic programming – A computational study