Traditional random access schemes are designed based on the aggregate process of user activation, which is created on the basis of independent activations of the users. However, in Machine-Type Communications (MTC), some users are likely to exhibit a high degree of correlation, e.g. because they observe the same physical phenomenon. This paves the way to devise access schemes that combine scheduling and random access, which is the topic of this work. The underlying idea is to schedule highly correlated users in such a way that their transmissions are less likely to result in a collision. To this end, we propose two greedy allocation algorithms. Both attempt to maximize the throughput using only pairwise correlations, but they rely on different assumptions about the higher-order dependencies. We show that both algorithms achieve higher throughput compared to the traditional random access schemes, suggesting that user correlation can be utilized effectively in access protocols for MTC.