We consider multi-objective ranking and selection problems with heteroscedastic noise and correlation between the mean values of alternatives. From a Bayesian perspective, we propose a sequential sampling technique that uses a combination of screening, stochastic kriging metamodels, and hypervolume estimates to decide how to allocate samples. Empirical results show that the proposed method only requires a small fraction of samples compared to the standard EQUAL allocation method, with the exploitation of the correlation structure being the dominant contributor to the improvement.