Simulation Allocation for Determining the Best Design in the Presence of Correlated Sampling

We consider the problem of efficiently allocating simulation replications in order to maximize the probability of selecting the best design under the scenario in which system performances are sampled in the presence of correlation. In the case of two designs, we are able to derive the optimal allocation exactly, and find that in the presence of positive correlation, unless the variance of one design is significantly larger than that of the other, the number of simulation replications should be identical. In extending to a general number of competing designs, an approximation for the asymptotically optimal allocation is obtained. The approximation coincides with the independent case derived previously in the limit as the correlation vanishes and also agrees with the two-design exact solution. Furthermore, the allocations prescribed by the results seem to match intuition, in terms of the relationship to correlations and relative variances between designs, again suggesting that equal allocation is optimal for sufficiently high positive correlation. An allocation algorithm based on the approximation is proposed and tested on several numerical examples.