We propose algorithms for allocating multiple resources to competing services running in virtual machines on heterogeneous distributed platforms. We develop a theoretical problem formulation and compare these algorithms via simulation experiments based in part on workload data supplied by Google. Our main finding is that vector packing approaches proposed in the homogeneous case can be extended to provide high-quality solutions in the heterogeneous case, and combined to provide a single efficient algorithm. We also consider the case when there may be bounded errors in estimates of performance-related resource needs. We provide a heuristic for compensating for such errors that performs well in simulation, as well as a proof of the worst-case competitive ratio for the single-resource, single-node case when there is no bound on the error.