Monte Carlo sampling-based methods are frequently used in stochastic programming when exact solution is not possible. A critical component of Monte Carlo sampling-based methods is determining when to stop sampling to ensure the desired quality of the solutions. In this paper, we develop stopping rules for sequential sampling procedures that depend on the width of an optimality gap confidence interval estimator. The procedures solve a sequence of sampling approximations with increasing sample size to generate solutions and stop when the width of the confidence interval on the current solution's optimality gap plus an inflation factor fall below a prespecified value,. We first present a method that takes the schedule of sample sizes as an input and provide guidelines on the growth of sample sizes. Then, we present a method that increases the sample sizes according to the current estimates of the optimality gap. The larger the estimates, the larger the increases in sample sizes. We provide conditions under which the procedures find-optimal solutions and terminate in a finite number of iterations with probability one and present empirical performance on test problems.

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