An improved averaged two-replication procedure with Latin hypercube sampling

The averaged two-replication procedure assesses the quality of a candidate solution to a stochastic program by forming point and confidence interval estimators on its optimality gap. We present an improved averaged two-replication procedure that uses Latin hypercube sampling to form confidence intervals of optimality gap. This new procedure produces tighter and less variable interval widths by reducing the sampling error by $\sqrt{2}$. Despite having tighter intervals, it improves an earlier procedure’s asymptotic coverage probability bound from ${(1?\alpha )}^2$ to $(1?\alpha )$.