Overlapping Batches for the Assessment of Solution Quality in Stochastic Programs

Abstract

Overlapping Batch Means (OBM) has long been used in simulation as a method of reusing data to generate variance estimators with asymptotically lower variance. In this article, we apply the OBM method to stochastic programming by formulating a variant of the multiple replications procedure used for assessing solution quality. We give conditions under which the resulting optimality gap point estimators are strongly consistent, the optimality gap interval estimators are asymptotically valid, and the OBM variance estimators for optimality gap have asymptotically lower variances relative to their nonoverlapping counterparts [Meketon and Schmeiser 1984; Welch 1987]. We investigate computational efficiency, a combined measure of variance and computation time, providing guidelines on the degree of overlap. Numerical experiments on several test problems are presented, examining the small-sample behavior and the empirical computational efficiency of the overlapping batches method in this context.